Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and...

focal pointDAVID W. HAHN AND NICOLO OMENETTO*

DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING

DEPARTMENT OF CHEMISTRY UNIVERSITY OF FLORIDA,

GAINESVILLE, FLORIDA

Laser-InducedBreakdown Spectroscopy

(LIBS), Part I:Review of Basic

Diagnostics and Plasma–Particle Interactions:

Still-Challenging IssuesWithin the AnalyticalPlasma Community

Laser-induced breakdown spectroscopy (LIBS)

has become a very popular analytical method in

the last decade in view of some of its unique

features such as applicability to any type of

sample, practically no sample preparation,

remote sensing capability, and speed of analy-

sis. The technique has a remarkably wide

applicability in many fields, and the number

of applications is still growing. From an

analytical point of view, the quantitative

aspects of LIBS may be considered its Achilles’

heel, first due to the complex nature of the

laser–sample interaction processes, which de-

pend upon both the laser characteristics and

the sample material properties, and second due

to the plasma–particle interaction processes,

which are space and time dependent. Together,

these may cause undesirable matrix effects.

Ways of alleviating these problems rely upon

the description of the plasma excitation-ioniza-

tion processes through the use of classical

equilibrium relations and therefore on the

Received 16 September 2010; accepted 30September 2010.

* Author to whom correspondence should besent. E-mail: [email protected].

APPLIED SPECTROSCOPY 335A

assumption that the laser-induced plasma is in

local thermodynamic equilibrium (LTE). Even

in this case, the transient nature of the plasma

and its spatial inhomogeneity need to be

considered and overcome in order to justify

the theoretical assumptions made. This first

article focuses on the basic diagnostics aspects

and presents a review of the past and recent

LIBS literature pertinent to this topic. Previous

research on non-laser-based plasma literature,

and the resulting knowledge, is also empha-

sized. The aim is, on one hand, to make the

readers aware of such knowledge and on the

other hand to trigger the interest of the LIBS

community, as well as the larger analytical

plasma community, in attempting some diag-

nostic approaches that have not yet been fully

exploited in LIBS.

Index Headings: Laser-induced breakdown

spectroscopy; LIBS; Ablation efficiency; Abla-

tion rate; Fluence; Irradiance; Local thermo-

dynamic equilibrium; LTE; Stark broadening;

Laser-induced fluorescence; LIF; Plasma diag-

nostics; Number density profiles; Temperature

measurements; Analytical sensitivity.

INTRODUCTION

The LIBS Community. As statedabove, a community centered around

laser-induced breakdown spectroscopy(LIBS) has clearly emerged during thelast decade. Indeed, LIBS has gainedenormous popularity and establisheditself as an analytical spectroscopic toolin several fields of applications. All thisis testified to by the number of confer-ences (see Table I) and resulting specialissues in international journals, books,book chapters, and reviews. Fourbooks,1–4 three of them having appearedin the last four years, are specificallydevoted to LIBS and its fundamentalprinciples, instrumentation, and applica-tions. Several other books are highlyrelevant to LIBS because they aredevoted to the spectroscopy of radiationsources in general and exhaustively treatthe theoretical foundations of spectros-copy, related instrumentation, and mea-surements. Among these, we cite herethe classic books on plasma spectrosco-py by Griem,5–7 the books of Fujimoto,8

Kunze,9 and Thorne,10 and severalbooks focusing on plasma diagnostics,e.g., Huddlestone and Leonard,11

Lochte-Holtgreven,12 and Bekefi.13 Oth-er useful books deal with specificemission sources such as direct current

(DC) arcs (Boumans14), flames (Alke-made et al.15), and inductively-coupledplasmas (ICP) (Montaser and Go-lightly16). The last two books cited inthis personal selection focus specificallyon laser microanalysis (Moenke-Blan-kenburg17) and laser interaction withmaterials (Miller and Haglund18).

The LIBS community is composed ofpeople with different backgrounds andareas of scientific expertise. Amongthem, there are those who are interestedin the basic understanding of the tech-nique (e.g., kinetic modelers, plasmaphysicists, plasma spectroscopists, fluiddynamicists), those who are interested inexploiting the unique characteristics ofLIBS, namely its remote sensing capa-bility applied to challenging importanttechnological and analytical problems(e.g., explosives, nuclear waste manage-ment, space exploration), and thoseinterested in the fields of geochemistry,industrial applications, cultural heritage,and forensic science. Much interest isdevoted to developing new instrumentaland analytical approaches aimed atincreasing the sensitivity of LIBS andalleviating the problem of matrix effects,

TABLE I. LIBS conferences resulting in Special Issues in international, peer-reviewed journals.

Conference Location and year Comments - Proceedings

LIBS 2000 8–12 October 2000, Tirrenia, Pisa (Italy) First conference dedicated to LIBS.Special issue: M. Corsi, V. Palleschi, E. Tognoni, Eds., Spectrochim. Acta,

Part B, volume 56, 565 (2001)EMSLIBS-I 2–6 November 2001, Cairo (Egypt) First European Mediterranean LIBS Conference.

Special issue: M. Harith, V. Palleschi, L. Radziemski, Eds., Spectrochim. Acta,Part B, volume 57, 1107 (2002)

LIBS 2002 24–28 September, Orlando, FL (USA) Special issue: D. W. Hahn, A. W. Miziolek, V. Palleschi, Eds.,Appl. Opt., volume 42 (30), 5937 (2003)

EMSLIBS-II 30 September–3 October 2003,Hersonissos, Crete (Greece)

Special issue: D. Anglos, M. Harith, Eds., J. Anal. At. Spectrom.,volume 19 (4), 419 (2004)

LIBS 2004 28 September–1 October, Malaga (Spain) Special issue: J. Laserna, N. Omenetto, Eds., Spectrochim. Acta,Part B, volume 60, 877 (2005)

EMSLIBS-III 6–9 September 2005, Aachen (Germany) Special issue: R. Noll, U. Panne, Eds., Anal. Bioanal. Chem.,volume 385, 212 (2006)

LIBS 2006 5–8 September, Montreal (Canada) Special issue: M. Sabsabi, R. Russo, Eds., Spectrochim. Acta,Part B, volume 62, 1285 (2007)

EMSLIBS-IV 10–13 September 2007, Paris (France) Special issue: A. Semerok, P. Mauchien, Eds., Spectrochim. Acta,Part B, volume 63, 997 (2008)

NASLIBS 2007 8–10 October 2007, New Orleans, LA (USA) First North American LIBS Conference.Special issue: J. P. Singh, M. Z. Martin, A. W. Miziolek, Eds., Appl. Opt.,

volume 47 (31), LIBS 1 (2008)LIBS 2008 22–26 September, Berlin Adlershof (Germany) Special issue: K. Niemax, U. Panne, Eds., Spectrochim. Acta,

Part B, volume 64, 929 (2009)NASLIBS 2009 13–15 July 2009, New Orleans, LA (USA) Special issue: J. P. Singh, J. R. Almirall, S. J. Rehse, Eds., Appl. Opt.,

volume 49 (13), LIBS 1 (2010).EMSLIBS-V 28 September–2 October 2009,

Tivoli Terme, Roma (Italy)Special issue: R. Fantoni, A. De Giacomo, Eds., Spectrochim. Acta,

Part B, volume 65, 591 (2010)LIBS 2010 13–17 September 2010, Memphis, TN (USA) Special issue: J. P. Singh, J. Almirall, A. W. Miziolek, Anal. Bioanal. Chem. (2011)EMSLIBS-VI September 11–15, 2011, Cesxme-Izmir (Turkey)

336A Volume 64, Number 12, 2010

focal point

as well as to testing well-established andnovel chemometric approaches.

Another LIBS Review? A very largenumber of reviews and chapters dealingwith the physical characterization ofplasmas and with the diagnostic ap-proaches to the evaluation of plasmaparameters such as temperature andnumber density of species exist in theliterature. Again, a personal selectionwas made, which covers a time span of45 years. As in the case of the previouslist of books, the references selectedhere cover both non-laser-based plasmasand plasmas induced by pulsed lasers,laser interaction with materials, andplasma formation. The references arelisted in chronological order.

The list19–56 includes specific chaptersdealing with non-laser-based plas-

mas,19–22,28,29,41 chapters on laser–mater-ial interaction,24,26,31,36,38,42 reviews onvarious aspects of non-laser-based plas-mas,30,32–35,40,43,45,51,56 and finally reviewson laser plasmas and laser–materialinteraction.23,25,27,37,39,44,46–50,52–55 Wemention here specifically the recentreview of Aragon and Aguilera,52 whichis highly relevant to the present article.

The field is still growing, however, ata rate that will make another overviewof the technique, with its clearly recog-nized advantages, but also with itsexisting problems and limitations, use-ful, if not totally warranted. An integrat-ed approach to the analytical anddiagnostic aspects of LIBS would re-quire a comprehensive discussion of themodeling efforts related to laser–materi-al interaction, plasma evolution, and

spectroscopic plasma characterization,to the interaction between the analyteand the plasma, and finally to thequantitative aspects of the technique(see Fig. 1).

In order to simplify the task, ourreview is divided into two parts. In thefirst part (this article), the discussion isfocused on the basic knowledge accu-mulated up to date on the theoreticalaspects of the technique, i.e., on thediagnostic characterization of the com-plex scenario of physico-chemical pro-cesses leading to the formation of ananalytical emission signal, in particularon the assumptions made and thespectroscopic tools used for such char-acterization. Therefore, topics such asablation efficiencies, local thermody-namic equilibrium (LTE), measurements

FIG. 1. An integrated approach to plasma spectroscopy, showing the major research topics addressed in the effort tocharacterize the plasma itself, the laser–sample interaction, the plasma–analyte interaction, and the quantitative aspects ofLIBS. The present article focuses on plasma diagnostics and plasma–analyte interactions.


of temperature and electron numberdensity, and especially the local plasmaperturbation effects resulting from thevarious interactions between the materi-al ablated and the plasma environmentwill be discussed in the first part. Theaim is also to offer the reader some basicwork and approaches that have beenpublished on other types of plasmas (notlaser induced) and that have not yet beenattempted in LIBS. The emphasis will begiven to what may be considered still-unsolved problems, both from the diag-nostics as well as analytical point ofview. Areas where improvement isneeded are identified, together with adiscussion of how to make such im-provement possible. Novel (from theLIBS point of view) approaches areoutlined and their relevance to theadvancement of our basic LIBS knowl-edge is evaluated.

The second part57 will have a moreapplied flavor and discuss more specif-ically instrumental and analytical ap-proaches (e.g., double- and multi-pulseLIBS to improve the sensitivity), cali-bration-free approaches, hyphenated ap-proaches (such as LIBS-Raman, LIBS-LIBS, LIBS-LIF) signal processing andoptimization (e.g., signal-to-noise anal-ysis), and applications. An attempt willbe made to provide an updated view ofthe role played by LIBS in the variousfields, with emphasis on applicationsconsidered to be unique. We will finallytry to assess where LIBS is going, wherein our opinion it should go, and whatshould still be done before attributing tothe technique the role of a superstar inthe field of chemical analysis.48

CHARACTERIZATION OF THELASER PARAMETERS ANDTHE ABLATION PROCESS

Description of Laser Light. Theconsiderations of this section refer tothe use of different terms describing theproperties of the (laser) light. Due to therather large amount of literature on laserablation and on LIBS, only a fewexamples of use of different terminologywill be given here. Some guidelinesrelated to the terms and notations to beused in LIBS in general and in particularin the description of laser parametershave been published.58

The terms used most frequently in the

literature are intensity, irradiance, flu-ence, radiant exposure, power (energy)density, volumetric energy density, and(occasionally) photon flux. Some of theabove terms are used interchangeably(e.g., radiant exposure and fluence, orintensity, power density, and irradiance).The units of intensity, irradiance, andpower density are power per unit area(W cm-2), while those of fluence andradiant exposure are energy per unit area(J cm-2). Finally, the units for thevolumetric energy density are energyper unit volume (J cm-3) and those ofthe photon flux are photons per unit areaper unit time (cm-2 s-1).

In terms of the symbols used, I, E, andP are commonly used for intensity,energy, and power, respectively. Ac-cording to the IUPAC nomenclature andin radiometry, the symbol E stands forirradiance and Q for radiant energy (see,for example, the book by Alkemade etal.,15 Appendix A.5, p. 943): on theother hand, the use of I is much morecommon, and E can be confused withenergy. The same applies for the ex-pressions describing the emission signalfor a given spectral transition (see TableIV). Fluence has been referred to asradiant exposure and given the symbolU0 or up (see, for example, Refs. 31 and46).

The use of terms such as powerdensity or fluence instead of irradianceshould be avoided. In any case, the unitsshould always accompany the parameterused: in fact, although it may be nameddifferently in different papers, the cor-rect parameter can always be identifiedfrom the units with which it is associ-ated. More importantly, since in mostcases pulsed lasers are used, the durationof the pulse dictates the relation betweenthe energy and the power in the beam.Fluence is indeed the time-integratedintensity or time-integrated irradiance.The pulse duration and shape aretherefore essential in the description ofthe interaction.

Table II collects several expressionsrelated to the above terminology. (Equa-tions given in this paper are referencedby the number of the table in which theyappear, i.e., T2.#.) According to theclassical definition of the properties oflight (see, for example, Menzel,59 pp.52–61), the relation between power (P),

intensity (I), and energy (E) is given byEqs. T2.1–T2.4, which are valid for anypulse shape. In these expressions, r, k,/, and t are the space vector, thewavelength, the polarization angle, andthe time, respectively. In Eq. T2.4, t0 isthe time corresponding to the center ofthe pulse temporal profile. The relationbetween the above quantities, and inparticular the experimental characteriza-tion of a pulse, is therefore not asstraightforward and requires sophisticat-ed detection apparatus. Equations T2.5–T2.7 are taken from Weyl31 and consid-er a temporal pulse shape that isGaussian, which is a good approxima-tion of a Q-switched laser pulse. The fullwidth at half-maximum (FWHM) of thepulse is given by Eq. T2.6 and theaverage pulse irradiance is related to thepulse fluence /p by Eq. T2.7.

Equations T2.5–T2.12 relate explicit-ly to the propagation of the laser beamand its focusing over the target and aretaken from Refs. 58–63. Assuming thatthe laser beam is cylindrical in shape,the length l, radius r, beam diameter d,beam divergence h, and focal length ofthe lens f used to focus the laser arerelated to each other by Eqs. T2.8 andT2.9. An important quantity to be takeninto account is the parameter M2, alsocalled beam quality or beam propaga-tion factor, which is given by the ratio ofthe beam parameter product of the actualbeam to that of a Gaussian beam(diffraction limited). The beam parame-ter product is the product of the beamdivergence h and the beam waist w0.59

All the above parameters enter theexpression T2.12, which allows theirradiance reaching the target to becalculated. It can be seen that theirradiance on the sample decreases asM2 increases from unity (.1).

Finally, Eq. T2.13 is relevant tomicro-LIBS and the minimum surfaceresolution achievable, as it is the well-known Rayleigh criterion for diffrac-tion-limited spatial resolution. Here, k isthe laser wavelength and NA is thenumerical aperture of the objective (see,for example, Refs. 63 and 64). Asreported by Sirven et al.,64 changingthe numerical aperture has a dramaticeffect on the signal and on the plasmashielding. It is important to recall herethat most analytical LIBS measurements


focal point

are performed with the laser focusedslightly below the sample surface. It hasbeen shown by Ciucci et al.65 thatimperfect focusing considerably affectsthe plasma and shock wave dynamics. Inlaser-ablated inductively coupled massspectrometry (LA-ICP-MS), Garcia etal.53 have indicated focusing slightlybelow the sample surface as a recom-mended strategy for optimum ablationand particle production.

The fact that most results are reportedin terms of laser fluence implies that theenergy is the parameter that matters indescribing the interaction (and is easierto measure). The conversion betweenpulse energy and power is simply madeby taking into consideration the pulsewidth (which is not always experimen-tally measured, but taken from themanufacturer data). We would like tostress again here what was pointed outby Haglund,66 namely that the ablationprocess has a complex convoluteddependence on both the pulse energyand the pulse duration. In this respect,not only should the total energy perpulse deposited on the target matter butalso the rate at which such energy isdeposited. In fact, it should be experi-mentally tested whether two pulsescharacterized by the same fluence butdifferent intensity profiles would pro-vide the same ablation efficiency andsensitivity.

This type of refined diagnostic is stilllacking in the LIBS literature. As onenotable exception, Aragon and Agui-lera67 made a careful series of experi-ments in which the laser energy wasvaried using an optical attenuator con-sisting of a half-wave plate that rotatesthe plane of polarization and a polariz-ing beam splitter cube, thereby preserv-ing the pulse width and its temporalshape.67

Ablation Efficiency. At first sight,the parameter ablation efficiency isassociated with a simple, intuitive con-cept. Yet, as illustrated in Fig. 2, theablation process is the result of acomplex interaction, involving laserparameters, sample properties, and plas-ma chemistry. As a consequence, theoverall description is far from beingsimple to rationalize or made applicableto all the different situations.

Table III collects several expressions

defining the ablation efficiency. A clear

understanding of this definition is per-

haps mostly relevant and needed in thefield of laser surgery for medical appli-

cations, for example, in removing clots

to restore blood flow while at the same

time maintaining vascular integrity, as in

laser thrombolysis,68 or in creating

channels in ischemic myocardium tis-

sues, as in transmyocardial revasculari-

zation.69 In a very comprehensive paper

dealing with pulsed laser ablation of

biological tissues, Vogel and Venugo-

palan46 discuss the concepts of ablationthreshold, Uth (J/cm2), ablation enthal-py, habl (J/g), ablation efficiency, gabl,

and their relation to the absorptioncoefficient of the tissue. The ablation

efficiency is defined as the amount ofmass removed per unit energy delivered

to the tissue and is expressed by Eq.T3.1 in Table III. In the above defini-

tion, q (g/cm3) is the density of thetissue, d (cm) is the etch depth, and U0 is

called the radiant exposure and isequivalent to the laser fluence (see later

below), with units of energy per unit

area (J/cm2). The ablation efficiency isusually reported in units of lg/J.

The authors46 also discuss the behav-ior of the ablation efficiency as a

function of laser fluence. This depen-

TABLE II. Examples of basic expressions characterizing the laser beam, its intensity distribution,its propagation, and its focusing behavior.

Expression DescriptionEquationnumber

P=R R R

Ipulseðr;k;uÞdudkdr Light power (Ref. 59, p. 52) T2.1

E=R R R R

Ipulseðr;k;u; tÞdtdudkdr Pulse energy (integrated over all distributions) T2.2

E=Z

pulse

PðtÞdt Power–energy relation of a pulse T2.3

t0=

Rpulse

tPðtÞdtR

pulsePðtÞdt

Time of the pulse center (i.e., when I(t) = Imax).This formula is valid for any pulse shape

T2.4

IðtÞ=I0exp -t2

s20

� �

Gaussian temporal profile (Ref. 31, p. 26) T2.5

sp=2s0

ffiffiffiffiffiffiffi‘n2p

FWHM (full width at half-maximum) (Ref. 31) T2.6

I=/p

sp

=Z þ‘

-‘

IðtÞdt

sp

=1:06I0 Average pulse irradiance (Ref. 31) T2.7

r=2kp

� �f

d

� �

Laser radius, diameter, length, and divergence(assuming a cylindrical shape) (Ref. 60)

T2.8

l=ðffiffiffipp-1Þh

df 2 Length and divergence assuming a cylindrical shape;

f = lens focal length (Refs. 60, 61)T2.9

w0h=ðk=pÞ Diffraction-limit condition (Ref. 59, p. 60) T2.10

M2=ðw0hÞbeam

ðw0hÞdiff lim

=pd0D‘

4f kBeam propagation factor (D‘ = lens diameter)

(Ref. 59, p. 60)T2.11

I=EppD2

‘

4spf 2k2

1

ðM2Þ2

" #

Irradiance at the target (equation derived fromthe various definitions given)

T2.12

Spot size=0:61k

NADiffraction-limited spot size (Refs. 62, 63) T2.13


dence differs considerably according totwo models considered, i.e., the ‘‘blow-off’’ and the ‘‘steady-state’’ models.46

The difference between the two modelsis mainly that, in the former, materialremoval is supposed to start after the endof the laser irradiation while in the lattermodel material removal occurs concur-rently with the irradiation. The lastmodel is therefore considered valid onlyfor long pulses (lasting a microsecond orlonger). A simple manipulation of theexpressions relating the etch depth, theabsorption coefficient of the tissue la

(cm-1), and the radiant exposure in thetwo models considered leads to Eqs.T3.2 and T3.3 in Table III. Basically, forfluences above a given threshold levelUth, the ablation efficiency increasesrapidly to a maximum and then decreas-es (blow-off model, Eq. T3.2), or itincreases and approaches a constant

plateau (steady-state model, Eq. T3.3)whose value is the reciprocal of theablation enthalpy. In both cases, if theproduct of the tissue absorption coeffi-cient and the threshold radiant exposureis constant, the maximum ablationefficiency is independent of the absorp-tion coefficient of the tissue. Thedecrease of the ablation efficiency athigh fluences in the blow-off case isattributed to the energy being wasted inoverheating the superficial layers of thetissue sample.46

The above terminology, includingterms such as ‘‘ablation rate’’, ‘‘ablationyield’’, and ‘‘ablation efficiency’’, havebeen addressed in a number of papersusing different types of lasers anddifferent pulse durations (fs-ps-ns), morespecifically related to LIBS or to laser-ablation inductively coupled plasmaoptical emission spectroscopy (LA-

ICP-OES) and/or LA-ICP-MS.70–78 Forexample, Salle et al.70 defined theablation efficiency as the ratio of thevolume of matter ablated (cm3) to thelaser pulse energy (J), while Semerok etal.72 referred to it as the ratio of thecrater depth (cm) to the laser fluence (J/cm2). These definitions can be simplyexpressed by Eqs. T3.4 and T3.5 inTable III.

In the above equations, Q‘ (J) is theenergy of the laser pulse, hs (cm) is thedepth of the crater, S‘ (cm2) is the laserirradiation area, and F‘ (J cm-2) is thelaser fluence. The obvious assumptionhere is that of an idealized cylindricalcrater profile, of surface area equal to thelaser spot area on the sample surface andof depth equal to hs. Indeed, when theabove two definitions are compared, itcan be seen that they are equivalent,provided that the intensity distributionof the laser corresponds to the craterprofile. This was correctly pointed outby Semerok et al.72 This problem ofequivalence has been specifically ad-dressed by St-Onge,73 who published asimple mathematical model describingthe influence of the laser beam radialenergy distribution on the depth profilesand on the crater aspect ratio. Becausethe laser beam profile is essential indetermining the quality of the depthresolution during the ablation process,the typical Gaussian profile of the beamis homogenized in a flat-top profile.75–77

Photothermal techniques have also ben-efitted from the use of top-hat laserprofiles.78

A comparison of Eqs. T3.1 throughT3.5 in Table III results in Eqs. T3.6 andT3.7. In the last two equations, thesuffixes VV and SS stand for Vogel–Venugopalan and Salle–Semerok, re-spectively. In essence, therefore, thetwo definitions are equivalent, with thedensity of the target material explicitlyshown in Eq. T3.7. One should relate theablated volume to the fraction that iseffectively removed in the ablationprocess, i.e., without including thematerial that may have been re-deposit-ed on the surface. Experimentally, it isfound for several target materials andlaser pulse widths that a plot of thecrater volume as a function of laserenergy and of the crater depth versuslaser fluence shows a linear dependence

FIG. 2. Overall pictorial view of the processes involved in laser ablation andplasma formation, together with their mutual correlation. The complex interactioninvolves laser parameters, sample properties, and plasma chemistry.


focal point

and a plateau depending upon the laserwavelength and the beam diameter (see,for example, Ref. 72 ).

In conclusion, it is clear that oneneeds a simple, unequivocal way ofcomparing experimental ablation datafrom different sources. In this respect,the measurement of crater volume and/or crater depth and laser pulse energyseems indeed the most logical approach.The resulting ablation efficiency wouldthen be a meaningful parameter, appli-cable to all experimental situationsencountered in practice with differenttypes of lasers, profiles, pulse widths,and materials.

There are two considerations, howev-er, that can be made. First, from a purelysemantic point of view, the term ‘‘effi-ciency’’ is generally reserved for param-eters that have no units, such as‘‘quantum efficiency’’ in the case ofphoton detectors or ‘‘detection efficien-cy’’ in the case of single atom/moleculedetection, i.e., a parameter characterizedby a number varying between zero andunity. On the other hand, it is fair to saythat the application of these classicaldefinitions to the ablation efficiency isnot straightforward, which explains whyno publications addressing new defini-tions and approaches have appeared onthis topic in more recent years. Onecould, perhaps, ratio the number ofatoms removed from the sample to thenumber of laser photons impinging onthe surface. This would be easy toimplement in the case of pure metaltargets, leading to Eqs. T3.8 and T3.9 inTable III (where NA, Ms, and hm are theAvogadro number, the molar mass, andthe photon energy, respectively). It iseasy to see that these last equations areequivalent to the previous ones, with theexception of the right-hand term inparenthesis in Eq. T3.9.

Another parameter, introduced byLucas et al.79–81 in their photo-fragmen-tation work to interpret the laser–particleinteraction energetic, is the ‘‘photon-to-atom ratio’’ (PAR), defined as the ratioof the number of photons striking theparticle to the number of atoms in theparticle. In aerosol-related work, thisparameter would be more useful than thefluence when comparing different sizedistributions.79 Its use, however, has notbecome popular in LIBS work.

Furthermore, with specific referenceto LIBS, it is clear that the ablationefficiency cannot be directly translatedinto emission intensity, unless the totalamount of removed material is vapor-ized and subsequently contributes to thespectral line emission measured, inabsence of self-absorption. This followsimmediately from the behavior of theablated volume as a function of laserenergy, where a single slope is notobtained and the graph levels off abovea given fluence. The ablation efficiencyis then characterized by a constant valuein the linear part of the plot and by a

subsequent continuous decrease whenthe plateau is reached (i.e., same ablatedvolume for increasing pulse energies).

In order to relate the ablation processto a quantity that has a better spectro-scopic relevance, the introduction of aparameter called ‘‘ablation sensitivity’’rather than ‘‘efficiency’’, was pro-posed.82 This parameter can be evaluat-ed from the graph obtained by plottingthe signal measured in optically thinconditions versus laser pulse energy.The units can be Volt/J, counts/J, orother suitable signal units divided byenergy units. Both the ablation efficien-

TABLE III. Definitions related to the ablation process and parameters involved.


gabl =qdU0

Ablation efficiency (Ref. 46, p. 611) T3.1

gabl =q

laU0

lnU0

Uth

� �

Ablation efficiency (blow-off model)(Ref. 46, p. 611)

T3.2

gabl =U0-Uth

hablU0

Ablation efficiency (steady-state model)(Ref. 46, p. 611)

T3.3

gabl =Volume ablated

Pulse energy=

S‘hs

Q‘Ablation efficiency (Ref. 70) T3.4

gabl =Crater depth

Pulse fluence=

hs

F‘=

hsS‘Q‘

Ablation efficiency (Ref. 72) T3.5

ðgablÞVV =mabld

VablU0

=mabldS‘S‘dQ‘

=mabl

Q‘Comparison T3.1 and T3.5 T3.6

ðgablÞSS =S‘hs

Q‘=

mabl

qQ‘Comparison T3.1 and T3.5 T3.7

gabl =Atoms removed per pulse

Photons per pulseAtom removal efficiency T3.8

gabl =qsS‘hsNAhm

MsQ‘=

qshs

F‘

NAhmMs

� �

Atom removal efficiency T3.9

dm

dt=

mass removed per pulse

ðunit areaÞðunit timeÞ Peak ablation rate (definition) T3.10

_mpeak =ms

S‘sL

Peak ablation rate (Ref. 85) T3.11

mave =ms

S‘sL

ðf‘sLÞ Average ablation rate(f‘ = laser repetition rate)

T3.12

dhs

dt= ð _hsÞpeak=

_mpeak

qs

Peak penetration rate (Ref. 85) T3.13

ð _hsÞave =_mave

qs

Average penetration rate T3.14

_m =q0dT

sL

Mass removal rate (Refs. 86–91) T3.15

_m = 110Ua

1014

� �1=3

k-4=3 Mass removal rate (Refs. 86–89) T3.16

_m = 2:66ðWÞ9=8ðIÞ1=2

ðAÞ1=4ðkÞ1=2ðsLÞ1=4Mass removal rate (Ref. 91) T3.17

W [A

2½Z2ðZ þ 1Þ�1=2Parameter entering Eq. T3.17; A = atomic mass;

Z = ionic charge (for singly charged ions Z = 1)T3.18


cy and the ablation sensitivity will beuseful to characterize the ablation pro-cess. However, the ablation sensitivitywill be more representative of the actualamount of material transferred into thevapor phase and contributing to plasmaemission. As an example of applicationof this definition, Amponsah-Manager etal.82 discuss the behavior of the ablationsensitivity and ablation efficiency as afunction of pulse energy for Cd and thebehavior of the ablation sensitivityversus laser energy for Cu. In the caseof Cd, the ablation sensitivity increaseswith pulse energy and subsequentlylevels off, while the increase in ablationefficiency is followed by a decreasewhen a given energy value is exceeded.The ablation sensitivity for Cd increasedinitially throughout the energy rangestudied, reaching a plateau of about 60 3106 counts/J at 50 lJ. The ablationsensitivity of Cu, however, reachedrather quickly a nearly constant plateau,indicative of an almost ideal situation, inwhich the emission intensity increases atthe same rate as the laser energy.82 As inthe case of the PAR parameter above,the concept of ablation sensitivity hasnot become popular in LIBS work.

Finally, we recall here that thedefinition of detection efficiency alreadyexists and is used in LA-ICP-MS work.The parameter is defined as the ratio ofions reaching the detector and thenumber of atoms released during laserablation and takes into account aerosollosses during transportation as well asincomplete vaporization in the ICP.83

Ablation Rate. Strictly connectedwith the ablation efficiency or sensitiv-ity, the ‘‘ablation rate’’ is another usefulparameter characterizing the ablationprocess. The parameter can be definedas the total mass ablated per unit timeper unit area and therefore has units of gcm-2 s-1, but the parameter can also bedefined as the ablated mass per unit area,ablated thickness per pulse, or ablatedmass per pulse (see, for example, Refs.74, 75, and 84). Although the discussionaccompanying most definitions is clear,the former one is preferable and shouldbe used when reporting this parameter,since it is directly linked to the conceptof rate. Obviously, one can convert themass per pulse into a peak rate by takinginto account the pulse width and into an

average rate by taking into account therepetition rate of the laser. However, thepeak rate during a single pulse might bedifficult to define (see below) and is noteasily amenable to direct experimentalobservation.

Table III collects several expressionsfor the ablation rate. Early in 1972,discussing the sputtering behavior ofglow discharges, Boumans85 had coinedseveral definitions which, with appropri-ate modifications, can also be useful here.To quickly convey the concept and for thesake of simplicity, we assume a rectan-gular laser pulse of duration Dt‘. Thus, Q‘

= P‘Dt‘. Adapting Boumans’ terminolo-gy to our purposes, parameters such as‘‘peak and average ablation rates’’ and‘‘peak and average penetration rates’’ canbe defined and are given in the expres-sions T3.10–T3.13. We can see that thepenetration rate has units of cm s-1. Allthe above parameters can be linked to thedefinitions of ablation efficiency andsensitivity given above. It is importantto stress, however, that Eqs. T3.10–T3.13are the only ones that assess the rate ofdeposition of energy to the target.

In addition, Table III also lists threeexpressions that have been reported inlaser ablation of foils and laser micro-analysis (see, for example, Refs. 36, 38,and 86–91). The symbols used are thetarget density (q0, g/cm3), the foilthickness (dT, lm), the pulse width (sL,ns), the ionic charge (Z), and the atomicmass (A, g/mol). Both Ua and Ia

represent the absorbed laser irradiance(W cm-2). These expressions have beenderived for very high irradiances (.1011

to 1012 W cm-2) and for short pulses(~10 ns), thus pertaining to the field oflaser-driven implosion. Interestingly,these expressions can be scaled downto the irradiances normally used in LIBSwork (~109 W cm-2) and are thereforedirectly applicable here. Indeed, thesame expressions have been reported inlaser microanalysis by Sappey andNogar38 and Dittrich and Wennrich.89

Note that the units of (dm/dt) in Eq.T3.16 are Kg cm-2 s-1, with Ua in Wcm-2 and k in lm, while (dm/dt) in Eq.T3.17 is given in lg cm-2 s-1, with k incm, sL in s, and I in W cm-2. Moreover,their predicted values have been com-pared and found to be in relatively goodagreement with the measured values in

the case of excimer laser (KrF) ablation,but not in the case of Nd:YAG abla-tion.70 Such extrapolations must there-fore be considered with caution whendifferent laser systems are involved.

Ablation rates, in terms of massablated per pulse, have been reportedby Iida84 for several types of materialsand for different pressures of argon asambient gas. The amount of materialvaporized, measured with a microbal-ance after 500 laser pulses, varied from7 ng/pulse in the case of W to 240 ng/pulse in the case of lead. Using theparameters reported by Iida84 (150 mJ/pulse at 1064 nm, 10 ns pulse width, anda spot size of 0.4 mm diameter), theexperimentally measured ablation ratecan be compared with that calculatedwith Eqs. T3.16 and T3.17. The values(expressed in lg cm-2 s-1) are 2.5 31010, 2.2 3 109, and 8.5 3 108,respectively. By considering the com-plexity of the laser–target interactionprocess, and the assumption that thelaser intensity reaching the sample andthat absorbed are the same, one canargue that an order of magnitudeagreement is satisfactory.

In conclusion, a unified approach tothe ablation efficiencies and rates is stillneeded. Even if such an approach can bemade, two main questions remain: First,the mass ablated and the useful massablated (i.e., that resulting in an emis-sion signal) may be largely different.Secondly, the chemical composition ofthe ablated mass in the plasma may bedifferent from that in the solid (i.e.,fractionation).

LOCAL THERMODYNAMICEQUILIBRIUM,THEORETICAL EQUILIBRIUMEXPRESSIONS, PLASMAPARAMETERS, AND THEIREVALUATION

The topics treated in this section,namely dealing with LTE considerationsand departure from equilibrium, with theequilibrium expressions used to describethe intensity of spectral lines and plasmacontinuum, and with the evaluation of thetwo most important plasma parameters(electron number density and tempera-ture), have been extensively discussed inthe literature. The relevant information iscollected in Tables IV through VII. These


focal point

tables are the result of scanning through alarge number of references, some ofwhich are listed in the tables. Neverthe-less, many more exist and therefore thoselisted reflect the personal choice of theauthors. As before, the articles citedcould be classified into two main groups:references that refer to non-laser-basedplasmas, and references in which thevarious methods have been applied toLIBS. In most cases, non-laser-basedplasma means microwave plasmas, ICP,high voltage sparks, DC arcs, flames, anddischarges. The choice of listing severalnon-LIBS references follows the spirit ofthis article, namely to remind the readerof very pertinent basic work availablebefore the LIBS literature ‘‘explosion’’.

References describing in detail theequations and methods listed in thesetables can also be found in various bookchapters and review articles: to cite just afew, for example, Zwicker,20 Lochte-Holtgreven,21 Cabannes and Chapelle,22

Mermet,28 Blades,29,30 van der Mul-len,32–34 Konjevic,43,56 Konjevic andRoberts,92 Eddy,93 Fincke,94 Jonkers etal.,95 and Calzada.96 With regard to thearticles cited, they can be divided intobroad categories dealing with populationdistributions and deviations from equi-librium,97–110 classification of diagnosticmethods,111,112 local and space-integrat-ed intensity definitions,113,114 ion-to-neutral ratios and their diagnostic rele-vance,115–125 line-to-continuum ra-tios,126–131 scattering methods,132–135

evaluation of electron number densityand plasma temperature, including Starkbroadening of H-lines,136–170 Starkbroadening of non-hydrogenic transi-tions,171–198 influence of the instrumentalprofile,199–204 calibration of the detectionsystem,205–213 interferometric214–220 andLangmuir probe measurements,221–224

nonlinear optical methods,225 and finallyabsorption and fluorescence meth-ods.226–259 Specific to LIBS , in additionto the books,1–4 we refer to the recentreview by Aragon and Aguilera.52

It is worth stressing that, since asignificant number of papers deal withnon-laser-induced plasmas, the directapplicability to LIBS of the approachdescribed must be considered withcaution, either because the LIBS valuesof the parameters are outside the dy-namic range of the method, or because

the transient character of the LIBSplasma and its unknown compositioncomplicates the interpretation of theexperimental results.

Local Thermodynamic Equilibri-um. The description of the plasma stateand the evaluation of its essentialphysical parameters are strictly connect-ed to the concept of thermodynamicequilibrium. This is described anddiscussed, to various degrees of com-plexity and theoretical detail, in theclassic literature cited above, to whichthe majority of specific articles dealingwith this concept always refer.

For a plasma to be in completethermodynamic equilibrium, all processesare balanced and characterized by a singletemperature. Therefore, the process ofexcitation of atoms by collisions withelectrons is equal to the reverse de-activation process (collisions of secondkind), collisional ionization is equal tothree-body collisional recombination, andradiation emitted is equal to the radiationabsorbed (see Lochte-Holtgreven,21

Chap. 3). When collisions dominate andthe same laws describing full thermody-namic equilibrium apply, but radiationdisequilibrium exists, we speak of com-plete local thermodynamic equilibrium.Considering that radiative transitionsbetween low-lying levels (resonancetransitions) are characterized by highvalues of the Einstein coefficient ofspontaneous emission, these levels aredepopulated much faster than corre-spondingly higher levels and are thereforemore prone to radiative disequilibrium. Ifthese levels are excluded, i.e., only levelsabove a certain main quantum number areconsidered in defining the requirementsfor attaining equilibrium, then we speakof partial local thermodynamic equilib-rium.21 This is the common situation withmost plasma sources.

As pointed out earlier, all the equa-tions reported in Table IV have beentaken or adapted from the literature.Since these are equilibrium expressions,LTE must hold in order for them to beapplicable. The first condition is that theelectron energy distribution function(EEDF) is a Maxwell–Boltzmann distri-bution. For this to be valid, the numberdensity of electrons must be less than acritical value, imposed by the constraintthat the mean distance between thermal

electrons should be less than the deBroglie wavelength K (see Fujimoto,8

Chap. 2, p. 22):

K =h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pmkTe

p

ne ðcm-1Þ � K-3=

2pkmTe

h2

� �3=2

ð1Þ

In Eq. 1, h is the Planck constant, m isthe electron mass, k is the Boltzmannconstant, and Te is the electron temper-ature (all units c.g.s.). If this is not thecase, quantum effects prevail and Fer-mi–Dirac statistics should be used. Fromthe above equations, ne needs to be lessthan 1021 cm-3 for Te = 6000 K and lessthan 6.7 3 1021 for Te = 20 000 K,conditions that are satisfied in mostlaboratory LIBS plasmas. At very highnumber density (~1022 cm-3), pressureionization causes the correction term inthe Saha equation to reach 100% of theionization energy.97 Even if such a highnumber density is not expected in LIBS,a more subtle and pronounced effectoccurs on the number of permittedlevels, as recently pointed out by DeGiacomo et al.98 In fact, even if thecorrection of the ionization energy isrestricted to a few percent, the numberof bound levels will be reduced to suchan extent that only a few lines will beseen in the emission spectrum. This wasshown to be case for hydrogen, wherethe Balmer series, for ne = 1019 cm-3,displayed only three lines.98

It is instructive to consider that all ofthe equilibrium relations require an idealplasma source in order to be applicableand tested. As pointed out by Wiese,35

in the late 1940s and 1950s physicistspursued the development of plasmasources with the goal of producing the‘‘ideal’’ source for plasma spectroscopy.Among others, one of the requirementsof such an ideal source was that it mustbe stable and stationary. It was indeedthe quest for such an ideal source thatled to the development of stabilized arcsources (wall, water, vortex stabilized),of the plasma jet and electrodelessdischarges, the ICP being the mostsuccessful among the last ones.35 In thisrespect, a laser-induced plasma, beingby definition a transient plasma, is notan ideal source for plasma spectrosco-


TABLE IV. Most useful and commonly reported formulas and definitions used in the LIBS plasma diagnostics literature. The expressions given refer tothe intensity of spectral lines and plasma continuum, to the criteria and definition of physical parameters relevant to the existence of (local)thermodynamic equilibrium, to the broadening of spectral lines, and to the relations used for the evaluation of plasma temperature and electron numberdensity.


ne‡1:6 � 1012ðTÞ1=2ðDEÞ3 McWhirter criterion, ne (cm-3); T (K); DE (eV) (Refs. 19,101)

T4.1

Tðt þ srelÞ-TðtÞTðtÞ � 1 Additional temporal condition for T; srel = relaxation time T4.2

neðt þ srelÞ-neðtÞneðtÞ

� 1 Additional temporal condition for ne T4.3

TeðxÞ-Teðx þ kÞTeðxÞ

� 1 Additional spatial condition for T; k = diffusion lengthduring srel

T4.4

neðxÞ-neðx þ kÞneðxÞ

� 1 Additional spatial condition for ne T4.5

r‘u =2p2

ffiffiffi3p

� �f‘u�ge4

1

2mem2

i DEu‘

0

B@

1

CA Cross-section of inelastic collisions (cm2); DE (erg); e

(statC); mi = electron velocity (cm s-1) (Ref. 101)T4.6

X‘uðTeÞ = nehr‘umi = 4pf‘ue4neh�gi

DEu‘

2p3mkTe

� �1=2

exp -DEu‘

kTe

� �

Collisional excitation rate (s-1); m = electron mass (g); k(erg K-1) (Ref. 101)

T4.7

srel »1

nehr‘umei=

6:3 � 104

nef‘uh�giDEu‘ðkTeÞ1=2

expDEu‘

kTe

� �

Relaxation time; the numerical value results from DE and kTin eV (Ref. 101)

T4.8

k = ðDsrelÞ1=2 » 1:4 � 1012ðkTÞ3=4

ne

DEu‘

MAf12h�gi

� �1=2

expDEu‘

2kT

� �

Diffusion length (cm); D = diffusion coefficient (cm2s-1);DE and kT in eV; ne (cm-3) (Ref. 101)

T4.9

eline =Au‘nuhm

4p

� �

Spectrally integrated line emissivity (Wcm-3sr-1) (Refs. 52,113)

T4.10

BmðmÞ =Au‘nuhm

4p

� �

SmðmÞ �1

Km

� �

Line spectral radiance (Wcm-2sr-1Hz-1) (Ref. 114) T4.11

Km [k�ðmÞ‘

1-exp½-k�ðmÞ‘�f g [sðmÞ

1-exp½-sðmÞ� Self-absorption factor: (Km), optical depth: s(m) (Ref. 114) T4.12

Bthermal = ðBÞPlankm0ðTpÞ �

Z

line

1-exp½-k�ðmÞ‘�f g Thermal line radiance (Wcm-2sr-1) k* = net absorptioncoefficient (Refs. 10, 15, 114)

T4.13

Ik;u‘ = Fexp

8phc

k3

nug‘n‘gu

� �R½1-e-kðmÞ‘�dm Integrated line irradiance (Wm-2) (Ref. 2, Chap. 3, p.

137—note a misprint here in the g’s ratio)T4.14

aj =ni;j

nj=

ni;j

ni;j þ na;j

ni;j

na;j=

aj

ð1-ajÞDefinition of degree of ionization, ni,j = na,j = ions (atoms)

number density of species j (Ref. 14, p. 157)T4.15

ðIþu‘ÞjðIu‘Þj

=gþu Aþu‘hmþu‘guAu‘hmu‘

� �

½ aj

ð1-ajÞ� Za;j

Zi;j

� �

expEu-Eþu

kT

� �

Ion-to-neutral ratio, (þ) refers to ion parameters, Eþu = fromion ground level (Ref. 14, p. 158)

T4.16

logaj

1-aj= log

Sn;j

ne

= -log ne þ3

2log T-

5040Ei;j

Tþ log

Zi;j

Za;jþ 15:684 Relation between ion-to-neutral ratio and ionization degree

(both T and ne can be evaluated) (Ref. 14, p. 164)T4.17

ne

ni

na

=2ð2pmekTionÞ3=2

h3

Zi

Za

exp -Eion-DEion

kTion

� �

Saha–Boltzmann equilibrium, Ti = ionization temperature;DEion = depression of Eion due to Debye shielding (Refs.10, 14, 15)

T4.18

Iu‘ = FexpAu‘gu

2Zi

½ h3

ð2pmkÞ3=2�neniT

-3=2ion exp

Eion-DEion

kTion

-Eu

kTexc

� �

Line ‘‘intensity’’, (energy/unit time - unit volume) (Refs.127, 128)

T4.19

ek;cont =16pe6

3c2ffiffiffiffiffiffiffiffiffiffiffiffiffi6pm3kp

� �neni

k2 ffiffiffiffiffiTe

p n½1-exp -hmkTe

� �

� þ Gexp -hmkTe

� ��

Continuum spectral ‘‘intensity’’ (energy/unit time - unitvolume - wavelength) (Refs. 127, 128)

T4.20


focal point

py. One may then wonder how LTEexpressions can be applied to a fast(~106 cm s-1) expanding plasma, with acorresponding expansion time, sexp, inthe microseconds range. On the otherhand, it is known that if energy issuddenly applied to a system, the systemrelaxes to a new equilibrium state in atime called the relaxation time, srelax,and is defined as (see, for example,Alkemade et al.,15 Chap. II, p. 59):

srelaxation=�N

m

=

Average number of gas kinetic collisions

per molecule needed to exchange energy

� �

number of gas kinetic collisions

per second per molecule

� �

ð2Þ

If srelax , sexp , equilibrium conditionsare warranted and the use of expressionspertaining to equilibrium is justified; ifthe contrary holds, the plasma is eitherionizing or recombining and there is nosimple description of the system withoutresorting to a full kinetic model. It is infact not surprising that the cautioningabout the existence of LTE in LIBS wasbrought to the attention of the LIBScommunity by scientists involved inkinetic modeling and the study ofelectron energy distribution functions(see, for example, Capitelli et al.47). Inthe case of a laser plasma formed on anAl target, and for early delay times (0.2–1.0 ls), Barthelemy et al.99 have calcu-lated that the expansion time of theplasma is about three to four timesshorter than the ionization time, thus

violating the LTE requirement. We notehere that, ideally, assuming that suchmeasurement will result in enoughsignal-to-noise ratio, one should inte-grate the signal for a time equal to therelaxation time.

The above considerations have beenquantified in several relations, as listedin Table IV. Equations T4.1 throughT4.9 are all relevant to LTE. EquationT4.1 is the most popular form of theMcWhirter criterion.19 There is hardly aLIBS publication that omits Eq. T4.1 inthe section dealing with the character-ization of plasma parameters. The cri-terion, originally derived in a differentform by Griem,100 refers to the mini-mum electron number density necessaryto ensure complete and partial localthermodynamic equilibrium, respective-ly, and requires that the collisional rate

TABLE IV. Continued.


Iu‘

ec

ðkÞ = h433=2c3

256p3e6k

� �Au‘gu

Zi

1

Te

expEi-DEi

kTe

� �

exp-Eu

kTexc

� �

½n 1-exp-hc

kkTe

� �

þ Gexp-hc

kkTe

� �

�

kDkmeas

� �

Line-to-continuum ratio (note that temperatures are keptdifferent) (Refs. 127–129)

T4.21

ne =DkStark � 109

2:5a1=2

� �3=2

= 8:02 � 1012Dk1=2

a1=2

� �3=2

Stark width–ne relation (linear Stark effect) (Refs. 112, 164) T4.22

ne =2ð2pmekTÞ3=2

h3

IuAþu‘gþu

Iþu Au‘gu

exp -Eion þ Eþu -Eu

kT

� �

Ion-to-neutral ratio–ne relation (see Eqs. T4.16, T4.18) (seealso Ref. 2, Chap. 3, p. 133)

T4.23

Dkwidth = wne

1016

� �

½1þ 1:75 � 10-4n1=4e að1-0:068n

1=6e T-1=2Þ� Stark width–ne relationship (quadratic Stark effect) (Refs. 21,

84, 173)T4.24

Dkshift = wne

1016

� �

½ d

w

� �

þ 2:0 � 10-4ðneÞ1=4að1-0:068n1=6e T-1=2Þ� Stark shift–ne relationship (quadratic Stark effect) [Refs. 21

(p. 135), 84, 173]T4.25

dmD

m0

=dkD

k0

=7:16 � 10-7

ffiffiffiffiffiT

M

r

Doppler spectral profile, M (g/mol) = atomic mass; T (K)(Refs. 10, 15)

T4.26

Dkres »3

16

g‘gu

� �1=2 k30e2f‘u

p2e0mec2

� �

n Resonance interaction broadening, e0 = vacuum permittivity(C2N-1m-2); c = speed of light (ms-1); n (m-3) (Ref.228)

T4.27

DkvanderWaals;width = 2:71C2=56 v3=5n

k2

cvan der Waals broadening (width), C6 = interaction constant

(m6s-1) (Ref. 228)T4.28

DkvanderWaals;shift = 0:98C2=56 v3=5n

k2

cvan der Waals broadening (shift), v = relative velocity

(ms-1) (Ref. 228)T4.29

T =Eu 0-Eu

k‘n

Iu 0‘ 0guAu‘

Iu‘gu 0 Au 0‘ 0

� �DT

T=

kT

DE

DRI

RI

þ DRA

RA

� �

Temperature evaluation from the line ratio and associatederror (Refs. 10, 15, 52)

T4.30

‘nIþu‘Au‘gu

Iu‘Aþu‘gþu

� �

= ‘n ½2ð2pmekÞ3=2

h3� T3=2

ne

� �( )

-ðEion-DEion þ Eþu -EuÞ

kTSaha–Boltzmann plot expression for evaluating plasma Texc

(Refs. 52, 150; see also Ref. 2, Chap. 3, p. 132)T4.31


TABLE V. A selection of different methods of evaluating the two most important plasma parameters: T and ne.a

Method (classification)bParameter(s)

measured Results and observations Selected referencesc

Absolute measurement of population density:absolute line intensity (ALI); atomic statedistribution function (ASDF); Passive –Indirect

T, ne Requires complete LTE; requires accuratetransition probabilities; requires absolutecalibration of the detection system. Thisapproach is difficult in the case of multi-element plasmas, where additionalmeasurements or known relations areneeded to determine local mixture ratios.35

Wiese35; Cabannes22; Mermet28; Van derMullen33; Jonkers95; Colao108

Absolute measurement of the plasmacontinuum; Passive – Indirect

Te, ne Requires partial LTE; Te needs to be knownto calculate ne and vice versa; requiresabsolute calibration of the detectionsystem.

Johnston126; Wiese35; Lochte-Holtgreven21;Cabannes22; Mermet28

Line-to-continuum ratio; Passive – Indirect Te, ne Requires partial LTE; requires accuratetransition probabilities; does not requirecalibration of detection system. The ratiocan be used to compare the Boltzmanntemperature with the electron temperature,thus assessing departure from LTE.128

Bastiaans127; Sola128; Liu129; Iordanova130,131

Two-line ratio measurement; Passive –Indirect

Texc Requires partial LTE; requires relativecalibration of the detection system.

Wiese35; Lochte-Holtgreven21; Cabannes22;Mermet28

Ion-to-neutral ratio; Passive – Indirect T, ne Requires complete LTE; requires accuratetransition probabilities; requires relativecalibration of the detection system. Thismeasurement is very often reported inLIBS work. Departure from LTE can beassessed by comparing the experimentalratio with that calculated in LTE. A classicexample is the use of the (Mg II/Mg I)ratio as a test element in ICP work.122

Wiese35; Cabannes22; Lochte-Holtgreven21;Bye115; Dennaud116; Corsi117; DeGiacomo118; Milan119; Grant120;Holclajtner-Antunovic121; Mermet122;Unnikrishnan148

Double ratio ion to neutral; Passive – Indirect T, ne Requires complete LTE; requires accuratetransition probabilities; requires relativecalibration of the detection system. It waspointed out that, for relatively lowtemperature and multi-element plasmas ofunknown composition, the combination ofthe line intensity ratio of two elements is abetter effective diagnostic tool.123 Theapproach was followed in LIBS workdealing with plasma–particle interactionstudies.124,125

Tognoni123; Diwakar124; Dalyander125

Boltzmann and Saha–Boltzmann plots;Passive – Indirect

Texc Requires partial LTE; requires accuratetransition probabilities; requires relativecalibration of the detection system. Notethat Boltzmann equilibrium populationsapply only to levels utilized in the plot:these levels may well be under- or over-populated against the ground state.35 Also,unless measurements are spatially resolved,the apparent temperatures obtained forneutral atoms and ions are different.156 Theconcept of apparent temperature waspointed out in flame work.145

Wiese35; Aragon52; Cabannes22; Mermet28;Caughlin104; Burton105; Calzada 106;Jonkers107; Aguilera156; Reif145

Vibro-rotational distribution from molecularspectra; Passive – Indirect

Tg (TVR) Requires partial LTE; requires transitionprobabilities. Measurements are performedusing emission bands, typically fromCN149 and C2.146 As in the case of atomictransitions, equilibrium takes time toestablish after plasma formation.

Lochte-Holtgreven21; Aragon52; Parigger146;Rusak149

Off-center measurement (Fowler–Milnemethod); Passive – Indirect

T Requires complete LTE; does not requiretransition probabilities; does not requirecalibration of the detection system. Theradial distribution T(r) is obtained. Such anapproach has not yet been attempted in alaser-induced plasma.

Wiese35; Lochte-Holtgreven21; Cabannes22;Mermet28; Pellerin154


focal point

TABLE V. Continued.



Optically thick plasma measurements (self-reversed lines)

T Requires complete LTE; requires accuratetransition probabilities. Self-reversed lineprofiles analysis is the basis for thisapproach. Models (two-zone168 orcontinuous distribution170) have beendescribed. Simultaneous data with a dualwavelength setup allowed obtainingvertical temperature profiles in a Baplasma.169 The approach has not becomevery popular in LIBS work.

Zwicker20; Lochte-Holtgreven21; Fishman40;Hermann168; Gornushkin169; Sakka170

Stark broadening, Stark half-width, Starkshift; Passive – (almost) Direct

ne Requires a Maxwellian distribution ofvelocities for electrons.35 This is valid inthe range of ne values found in LIBS. Thistopic is one of the most relevant in thecharacterization of LIBS plasmas. As aresult, most papers report Stark broadeningequations for the evaluation of ne and itstemporal evolution in the plasma. All H-transitions (including Lyman lines144) havebeen measured, in addition to several non-hydrogenic lines (see Table VI).

Konjevic43; Luque136; Griem137; Kepple138;Thomsen139; Acon140; Gigosos141,142;Starn143; Fussmann144

Stark ‘‘intersection method’’; Active –(almost) Direct

Te, ne Requires a Maxwellian distribution ofvelocities for electrons.35 The approachallows the simultaneous determination oftemperature and electron number densityusing hydrogen Balmer lines.

Yubero166; Sola167; Torres112

Scattering methods (Rayleigh and Thomson);Active – (almost) Direct

Te, Tg, ne Requires a Maxwellian distribution ofvelocities for electrons.35 Despite someinstrumental complexity, Thomsonscattering is the most accurate, local, andunambiguous way to determine ne.

132

Dynamic range of Thomson scattering:1012–1016 (cm-3).132 SimultaneousThomson and Rayleigh scatteringmeasurements provide space- and time-resolved values of Te, Tg, and ne in theICP.134 Te and ne images have beenobtained in a microwave plasma torch.133

Time-resolved LIBS images showed thatscattering vanished at delays of ~100ns.102 Rayleigh scatter by ground-stateargon atoms was used to evaluate Tg in aDC arc.135

Warner45; Diwakar102; Meulenbroeks132;Prokisch133; Huang134; Murphy135

Interferometric methods; Active – Direct ne, atomnumber density

Do not require LTE. Methods are based onthe analysis of fringe structures. Electronnumber density can be determined at earlydelay times. Data have been reported onplasmas made by laser ablation on Al215,Mg216, and Ti218 targets, in addition to insitu depth profile mapping.219 A distinctadvantage is that no LTE assumption isneeded.214 Finally, absolute number densityof laser-ablated Cu atoms were obtainedusing ‘‘hook spectroscopy’’.220

Hearne214; Ni215; Doyle216,218; Harilal217;Papazoglou219; Sappey220

Electrical current measurements (Langmuirprobes); Active – Direct

Te, ne Metal probes are placed several cm awayfrom the laser plasma. Time-of-flightprofiles of electrons can be obtained soonafter plasma formation. Te is derived fromthe slope of the plot (I/V),221 while ne isderived from the saturation region of the(I/V) characteristics.223 Experiments werecarried out on plasma formed by laserablation of Ag221, Cu223, and Al targets.224

These ultrafast, non-contact diagnosticmethods are more relevant to the study oflaser–target interaction than to plasmadiagnostics.

Issac221; Long222; Weaver223; Amoruso224


is at least ten times larger than theradiative rate.19 Many conclusions de-rived from the application of theMcWhirter criterion have recently beenput under scrutiny.101 The criticism wasprompted by the fact that many generalstatements can be found in the literatureindicating that LTE conditions existbecause the lower limit for ne calculatedfrom Eq. T4.1 is well below theexperimental value measured from Starkbroadening (see below). Some papersadd to the above conclusions a warningsaying that the criterion is a necessary,but not sufficient, condition for LTE.Finally, some papers report additionalmeasurements supporting the conclusionthat LTE can indeed be safely assumed.As pointed out earlier, it is important torealize that the criterion was derived forstationary, homogeneous, and opticallythin plasmas.19 Equations T4.2 throughT4.5 illustrate the two additional re-quirements that need to be fulfilled. Inthe time domain (Eqs. T4.2 and T4.3),the temporal variation of Te and ne

should be small compared to the timetaken to establish excitation and ioniza-tion equilibria, while in the spacedomain (Eqs. T4.4 and T4.5), thevariation length of Te and ne should belarger than the distance traveled by aparticle due to diffusion during therelaxation time.101

The remaining four equations (Eqs.T4.6 through T4.9) can be used to

calculate the cross-section, r‘u, forinelastic collisions (Eq. T4.6), the rateof collisional excitation and de-excita-tion, X‘u, resulting from averaging thecross-section over the Maxwellian dis-tributed electron kinetic energies (Eq.T4.7), the relaxation time, srel (Eq.T4.8), and the diffusion length, k, duringthe relaxation time (Eq. T4.9). For adiscussion of each of these parametersand their derivation, the reader isreferred to Cristoforetti et al.,101 wherethe original references are reported.Calculations from literature data haveshown that the diffusion length criterionis verified for copper, iron, and nickel,because the values obtained are muchlower than the plasma dimensions, butcannot be fulfilled in the cases ofhydrogen and oxygen.101 EquationT4.8 is useful because it allows a quickestimate of the relaxation time expectedfor a given transition, characterized byan absorption oscillator strength f‘u andenergy difference DE‘u, and a plasmacharacterized by an electron numberdensity ne and temperature Te. Caremust be taken in assuming that theaverage Gaunt factor h�gi is unity,because its value depends upon the ratioin the exponent of Eq. T4.8.101 Asexpected, weak, low UV transitions inplasmas of moderate values of ne and Te

result in longer relaxation times and aretherefore more prone to non-equilibriumeffects.

In conclusion, the McWhirter criteri-on alone, even if satisfied, is notsufficient to ensure LTE conditions. Atshort delays, ne is much larger than thatcalculated with Eq. T4.1, while at longerdelays, the minimum criterion may notbe reached. What this means is that, atlonger delays, LTE conditions do notexist, while at shorter delays, LTE mayexist, provided that the other conditionsregarding equilibration times and plasmainhomogeneities are satisfied. This ishardly satisfied at early delay times in aLIBS plasma, due to the high plasmafree electron gradients, as shown exper-imentally by Diwakar and Hahn usingThomson scattering.102

From the discussion of the variousexperimental conditions, it was thereforesuggested101 that the mere use of theMcWhirter criterion to prove the exis-tence of LTE should be abandoned.

Deviations from equilibrium are nor-mally represented by the parameter b(p),which is defined as the ratio between thepopulation of the level actually mea-sured and the value given by the Saha–Bol tzmann equi l ibr ium expres-sion,103–108 i.e.,

bðpÞ = nðpÞnSBðpÞ

ð3Þ

If b(p) is greater or lower than unity, theplasma is in an ionizing or recombiningstate, respectively. The reduced popula-

TABLE V. Continued.



Laser-induced absorption methods;Active – Direct and Indirect

Texc, ne, numberdensity of levels(including theground state)

See Table VII See Table VII

Laser-induced fluorescence methods;Active – Direct and Indirect

Texc, ne See Table VII See Table VII

Nonlinear optical methods; Active – Directand Indirect

Number density,Texc, Te

Approaches such as two-photon excitation(fluorescence), double-resonant four-wavemixing, and coherent anti-Stokes Ramanscattering (CARS) belong to thiscategory.225 Methods can be direct orindirect, depending upon the chosenmeasurement scheme. Detection of atomicH is a classic example of application of thetwo-photon excited fluorescencetechnique.225

Ochkin225

a This table (in expanded format) is similar to that published by Wiese.35

b The method classification follows the definitions of de Regt et al.111 and Torres et al.112

c This column reports the name of the first author appearing in the reference cited.


focal point

tion density of the ground state, definedas the population density divided by thelevel statistical weight, is also used todefine how close the plasma is to LTE.Overall, b(p) should range between 1and 10.103

From the above articles,103–108 thefollowing considerations are summa-rized here. If one refers to the expressionfor the integrated spectral emissivity andradiance of an optically thin line (seeEqs. T4.10 and T4.11 in Table IV), it isclear that an absolute measurement ofthis quantity, i.e., an absolute lineintensity (ALI) measurement, will allowthe derivation of n(p). Such measure-ment can be repeated for differenttransitions originating from levels atincreasing excitation energies. The plotof the absolute number density of theexcited state versus the energy of theupper level represents the atomic statedistribution function (ASDF). If aBoltzmann equilibrium distribution isassumed among the various levels, theratio of any two lines will give anexcitation temperature, and so will theslope of the line obtained by connectingthe various number density values(Boltzmann plot). The advantage hereis that, because absolute number densi-ties have been measured, one can add tothe graph the ground state (En = 0)number density, calculated from theideal gas law, and using the rotationaltemperature of the main gas species asthe gas temperature.107 The line con-necting this point and the lowest of thenumber densities calculated before willindicate whether the slope obtained isthe same, higher than, or lower than thatwhich connects the populations of theexcited levels. If the slope is the same,the system is in LTE, while if the slopeis higher or lower, the plasma is ionizingor recombining, respectively (see Fig. 3,top left).

The measurement of ASDFs is acommon practice in several types ofnon-laser-based plasmas,103,106,107 butvery few measurements have beenreported in LIBS, see for example Ref.108. This can be attributed not only tothe difficulty of performing absolutenumber density measurements, butmainly to the practical difficulty incalculating the number density of theground state of the atomic species in the

plasma. Another reason is that lowenergy levels are more prone to self-absorption effects. We note here thatabsorption measurements would providea distinct advantage here (see TableVII).

The most important theoretical impli-cation is that a straight line connectingthe points starting from a given excita-tion level cannot guarantee a uniquetemperature value, since the lowerenergy part of the line is missing. Forexample, in the case of an argon plasmaproduced by the microwave-driven plas-ma torch (called ‘‘torche a injectionaxiale’’107), from the slope of theBoltzmann plot obtained using levelslying in the range 13–16 eV above theground state, a temperature of 4860 Kwas calculated. However, when theground-state number density was includ-ed as an additional point in the plot, thetemperature was much higher107 (seeFig. 3, bottom panels).

Equilibrium Expressions and Diag-nostic Methods for the Evaluation ofT and ne. The ideal diagnostic methodwould be one characterized by thefollowing features: (1) it does not relyupon the assumption of LTE; (2) it doesnot require knowledge of the fundamen-tal constants (e.g., radiative transitionprobabilities); (3) it does not necessitatethe calibration of the detection system;and finally, (4) it should be relativelyeasy to implement in common laborato-ry practice. A method possessing all ofthe above requisites is hard to find.

Table V reports a number of diagnos-tic methods. The format of the table issimilar to that given and discussed byWiese.35

De Regt et al.111 and Torres et al.112

have classified the methods as direct orindirect, and as active or passive.Methods are considered ‘‘direct’’ whenthey allow the value of the parameter ofinterest (T, ne) to be obtained withoutmaking any assumption about the typeand degree of equilibrium existing in theplasma. ‘‘Indirect’’ methods must as-sume some type of distribution for theparticles in the plasma and for theirexcitation-ionization stages. In addition,‘‘active’’ methods use external sources toprobe the plasma (e.g., in Thomsonscattering experiments), while ‘‘passive’’methods use the plasma itself to measure

the parameter of interest (e.g., absoluteline emission measurements).111,112

Indirect methods suffer from theinherent contradiction that their use isconditional upon the existence of theproperty that they are supposed tocheck. On the other hand, one cancompare several indirect methods witheach other and find a consistency or atleast a recognizable trend in the resultsprovided by each method. For example,under LTE, the application of theBoltzmann plot method to several ele-ments individually will always give thesame slope and therefore the sametemperature. Alternatively, several ele-ments can be used to construct a singleplot (multi-element Boltzmann plotmethod), after proper correction for thedifferent concentration of each elementin the sample (assuming equal stoichi-ometry in the solid and gas phase) andfor their different ionization degree inthe plasma (see Table V for the pertinentreferences).

Active methods need not be directmethods. For example, the two-linefluorescence approach to the evaluationof the plasma temperature is based uponthe existence of LTE, since the popula-tion of the levels is given by theBoltzmann distribution.

The most common expressions for theemission signals due to line (bound–bound) transitions and continuum (free–free) transitions are shown in expres-sions T4.10 through T4.21. In all theequations, the subscripts u and ‘ standfor the upper and lower level of atransition, and the superscript ‘‘þ’’ refersto ions. Equation T4.10 refers to thespectrally integrated line emissivity (Wcm-3 sr-1),52,113 denoting a spatiallyresolved local value. Note that this isdifferent from Eq. T4.11, which refers tothe spectral radiance (W cm-2 sr-1

Hz-1):114 here, integration over distancehas been performed, and thus a uniformspatial distribution of atoms (ions) hasbeen assumed in a length of plasma (‘)along the direction of observation. InEq. T4.12, K is the self-absorptionfactor (no units) and is a function ofthe optical depth s(m) (no units, despitethe ‘‘length’’ concept), of the absorptioncoefficient k*(m) (cm-1) and of ‘ (cm).The asterisk over k(m) indicates thatstimulated emission is taken into ac-


TABLE VI. Determination of electron number density and Stark coefficients using Stark broadening of neutral and ionic transitions other thanhydrogen. The data reported here refer solely to measurements taken with laser-induced plasmas on different targets and in different gas environments.a

Element Spectral linesb (nm) Experimental arrangement: observations Referencec

Al I 394.400, 396.152 Generally, a Q-switched Nd:YAG at 1064 nm was used.Targets were solids (in air or in pressure-tight chambers)and liquids172 (remote measurements). Stark shifts werealso considered84,170 and self-reversed emission profileswere calculated.170

Samek172; Zhao173; Ying174; Iida84;Sakka170

Al II 199.053, 263.155, 266.916, 281.619,390.068, 466.306, 559.330

Pulsed Nd:YAG at 1064 nm (200 mJ, 7 ns) focused on anAl target (99.9999% purity) in vacuum.175 Starkbroadening parameters were determined for all lines.175

Generally, Nd:YAG lasers were used, except in Ref. 99(IR Ti:Sapphire and a XeCl lasers). In Ref. 177, the Haline was used for comparison.

Colon175; Galmed176; El-Sherbini177;Barthelemy99; Sabsabi147

Ar I 696.543, 703.025, 706.722, 727.294,738.398, 751.465, 763.511, 772.376

Ruby laser (1.5 J/pulse, 30 ns, 4 Hz, 694.3 nm) focusedinside a stainless-steel chamber filled with Ar at 800 mbar.

Hanafi178

Q-switched Nd:YAG (250 mJ/pulse, 15 ns, 1064 nm)focused inside a stainless-steel chamber filled with Ar atatmospheric pressure.

Cadwell179

Ar II 396.836, 401.386, 433.120, 434.806,476.487, 480.602, 484.781

Ruby laser (5 J/pulse, 22 ns, 694.3 nm). Measurement carriedout in a plasma created in argon (a high-pressure puff ofargon passing through a nozzle) with the addition of He.Electron number density calculated using the He I transitionat 587.562 nm and the He II transition at 468.57 nm.

Iglesias180

Au II 192.100, 204.459, 221.316, 221.564,223.121, 228.331, 229.141, 230.468,231.455, 231.575, 234.008, 255.267,256.270, 268.761, 268.815, 280.204,281.979, 282.544, 283.785, 290.704,291.352, 295.422, 298.210, 299.027,299.480, 301.581

Q-switched Nd:YAG (160 mJ/pulse, 7 ns, 20 Hz, 1064 nm)focused on a gold target in a chamber filled with Ar, He,and N2 at 6.5 Torr.

Ortiz181

Ba I 553.548 Q-switched Nd:YAG (9 ns, 10 Hz, 1064 nm) focused onto amulti-element YBa2Cu3O7 target in a vacuum chamberkept at 0.01 Pa.

Harilal182

C I 505.217 ArF (440 mJ/pulse, 20 ns, 10 Hz, 193 nm) laser ablation ofa graphite target in vacuum.

Hoffman183

C II 723.132, 723.642 Hoffman183

Ca I 422.673 Q-switched Nd:YAG (100–300 mJ/pulse, 10 ns, 20 Hz, 1064nm) remotely delivered on a liquid sample surface.

Samek172

Cl I 837.594 Q-switched Nd:YAG (25–100 mJ/pulse, 4–8 ns, 10 Hz, 1064nm) focused on BeCl2 (nebulization) and Be (laserablation) particles.

Radziemski184

Cu I 521.820 Q-switched Nd:YAG laser (1064 nm, 8 ns, 10 Hz) focusedon a copper target (99.999%) located in 0.8 T steadymagnetic field.

Yu Li185

F I 685.603 See Cl I Radziemski184

Fe I 381.584, 538.337 Nd:YAG focused on a low-alloyed steel target in air, argon,and helium at atmospheric pressure. Asymmetric Starkbroadening study of the 538.337 transition.186 Influence ofthe static ion effect. Spatially and temporally resolved data

Bengoechea186,187; Monge188;Aguilera189

He I 388.865, 587.562 See Ar I and II Hanafi178; Iglesias180

He II 468.57 See Ar I and IILi I 610.353 Pulsed Nd:YAG at 1064 nm (20 ns) focused on a LBO

crystal target.Hou190

Mg I 470.299, 516.732, 552.840 Q-switched Nd:YAG laser (10 mJ/pulse, 1064 nm, 8 ns)focused on the target inside a chamber filled with Ar at140 hPa.

Zhao173

Mn I 279.482, 403.076, 403.307, 404.136,476.238

Q-switched Nd:YAG emitting two variably delayed collinearpulses (60 mJ/pulse, 12 ns, 1064 nm). Effect of self-absorption on Stark profiles was studied. Stark coefficientshave been measured for several lines.

Bredice191

Mn II 259.373, 260.569, 293.306, 293.930,294.920, 344.199, 348.291, 261.020,270.170

See Mn I Bredice191

N I 746.831, 415.148 See Ar I and II Hanafi178

See Cl I Radziemski184

Q-switched ruby laser at 693.4 nm (1.5 J/pulse, 30 ns)focused in He, Ar, N, and air. Laser-induced NaCl–waterplasma.

Hannachi192


focal point

count. Integration of Eq. T4.11 overfrequency removes the spectral distri-bution function, S(m), due to its normal-ization. Moreover, using the classicaldefinitions for k(m) and the relationsbetween the Einstein coefficients, Eq.T4.13 is obtained. This is the expressionfor the thermal radiance of a transition,which shows that the measured emissionsignal increases with concentration aslong as s(m) ,, 1 and is bound to itsmaximum value given by the Planckblackbody radiation when s(m) .. 1.All the above considerations are wellknown and are part of the curve-of-growth theory (see, for example, Refs.10 and 15).

Note that, in addition to the assump-tion of uniform atomic distribution, thetemperature of the system is alsoassumed to be uniform here. As a result,self-absorption will gradually broadenthe line profile without showing a dip inthe line center. When such a dip isobserved, it means that a temperaturegradient exists along the direction ofobservation and the profile is then self-reversed. Self-reversal is sometimesreferred to as an extreme case of self-absorption; however, the two terms havea basic different meaning. In LIBS

work, self-reversal is easily observedfor strong transitions involving theground state (see Fig. 4). It is worthmentioning that sometimes the dipcannot be discerned experimentally: thisis either due to the fact that the spectralresolution of the monochromator is notadequate enough or because the overalleffect has been smoothed out by thespatial and temporal averaging causedby the detection system.

Finally, we note that optically thick,self-reversed transitions can be advanta-geously used in plasma diagnostics (seeTable V).

Equation T4.14 is an intermediateform of Eq. T4.13, used in experimentalLIBS work. This expression reverts tothe previous one when the Boltzmannexpression is used for the ratio (nu/n‘)and the Wien law (i.e., negligiblestimulated emission) is used for theblackbody radiation. The units of Ik,u‘

are W cm-2. As noted before, these arethe units of the term irradiance; how-ever, the term intensity is used synony-mously.

Equation T4.15 is simply the defini-tions of the degree of ionization for thespecies j in the plasma, ni,j and na,j

indicating the ion and neutral atom

number density, respectively. Thesedefinitions are used in Eqs. T4.16 andT4.17, which relate the ion-to-neutralratio to parameters such as the ionizationpotential (Ei), partition functions (Z),and transition probabilities (A). Theformulation expressed by Eq. T4.17 istaken from Boumans14 (Chap. 7, p.164).

Equations T4.19 through T4.21 arethe basic expressions used for the line-to-continuum ratio. Equation T4.21 re-sults from the combination of Eq. T4.19with the Saha ionization equilibriumexpression (Eq. T4.18).

The reason for presenting these ex-pressions individually stems from thefact that we would like to emphasize thatdifferent temperatures should be used ineach expression: the excitation temper-ature (Texc) for the line intensity, theionization temperature (Ti) for the Sahaequilibrium, and the electron tempera-ture (Te) for the intensity of thecontinuum. Ti is assumed to be equalto Te. Equation T4.20 contains twocorrection factors, namely the free–freeGaunt factor (G) and the free-boundcontinuum factor (n), both derived fromquantum mechanical considerations(see, for example, Refs. 127 and 128).

TABLE VI. Continued.

Element Spectral linesb (nm) Experimental arrangement: observations Referencec

N II 343.715, 395.585, 399.500, 500.148 See Cl I Radziemski184

Q-switched Nd:YAG focused on a polished Ti alloytarget.193 In Ref. 102, Stark data compared with Thomsonscattering at very early plasma dynamical evolution (100 ns).

Man193; Diwakar102

Pb I 217.000, 223.743, 244.618, 283.305 Q-switched Nd:YAG laser (275 mJ/pulse, 7 ns, 20 Hz, 1064nm). Sample: Sn-Pb alloy in a vacuum chamber filled withAr at 6 Torr. Only one wavelength reported per transitionarray. Quasi-static ion broadening neglected.

Alonso-Medina194

Si I 288.158 Laser ablation in the cavity. T and ne increase withincreasing cavity aspect ratio.

Zeng195

Si II 504.103, 595.756, 597.893, 634.710,637.136

Q-switched Nd:YAG laser (250 mJ/pulse, 10 ns, 1064 nm)focused on 99.9% pure SiO2 target inside a stainless steelvacuum chamber.

Wolf 196

Sn I 317.505, 326.234 Q-switched Nd:YAG laser (240 mJ/pulse, 7 ns, 1064 nm)focused on a Sn target inside a vacuum chamber filled withAr at 6 Torr.

Martinez197

Sn II 299.444, 347.246, 353.757, 358.239,362.054, 371.523, 384.144, 487.722,494.431, 559.620, 579.918, 645.350

See Sn I Martinez197

Zn I 334.502 Q-switched Nd:YAG forming a Zn plasma in air at threewavelengths 1064 nm (450 mJ/pulse), 532 nm (200 mJ/pulse), and 355 nm (90 mJ/pulse).

Shaikh198

a This table is complementary to that reported in the review by Aragon and Aguilera.52

b Note that the wavelengths reported have been corrected using the NIST Atomic Spectra Database (version 3.1.5), [online]. Available at http://physics.nist.gov/asd3[2010, July 29]. National Institute of Standards and Technology, Gaithersburg, MD.

c This column reports the name of the first author appearing in the reference cited.


If both factors are close to unity, theexpression in brackets is also unity: thisoutcome, however, should be consideredwith care.101

The line-to-continuum ratio (Eq.T4.21) is a very useful parameter inplasma diagnostics. An interesting ap-proach has been discussed by Sola etal.128 and applied to a microwaveplasma. The idea consists of experimen-tally obtaining the ratio resulting fromthe measurement of a line transition andthe underlying continuum and theninserting this value into Eq. T4.21,where the two parameters Te and Texc

are purposely maintained different fromeach other (note that usually only asingle temperature appears in Eq. T4.21,because the assumption is made that Te

= Texc). If Texc is now measuredindependently by the Boltzmann ap-proach, two experimental values areavailable (Texc and the ratio), whichcan both be inserted into Eq. T4.21. Te

can now be calculated and comparedwith the value of Texc obtained by theBoltzmann plot. The discrepancy be-tween the two values can be attributed toa departure from LTE. Figure 5 showssome experimental results obtained in aplasma created on a brass sample.

Note that, since the line and thecontinuum are measured practically atthe same wavelength, no calibration ofthe detection system is necessary. On theother hand, it should be stressed that theunits used in the theoretical definitionsof the line intensity and the continuumspectral radiance are different, since theline is integrated over the entire emis-sion profile while the continuum spectralradiance is given per unit wavelength.Experimentally, both the line and thecontinuum are spectrally integrated. Thedifference between the theory and ex-periment must therefore be taken intoaccount: this explains the factor Dkmeas

appearing in the last factor of Eq. T4.21.The above approach can be consid-

ered another example of the inherentcontradiction of using equilibrium ex-pressions to check whether equilibriumexists. Nevertheless, two parameters,Texc and the ratio (Iu‘/ec), are measuredindependently.

Equations T4.22 and T4.23 show howthe electron number density is calculatedfrom the Stark broadening of the

hydrogen transitions and from a mea-surement of the ion-to-neutral ratio,while Eqs. T4.24 and T4.25 refer tonon-hydrogenic transitions, several ofthem being collected in Table VI.Equations T4.26 through T4.29 are theexpressions commonly used to describethe physical line width corresponding tothe various broadening mechanisms.The last two expressions, T4.30 andT4.31, refer to the evaluation of theplasma temperature by the two-linemethod (or by extrapolation to manylines by the Boltzmann method) and bythe Saha–Boltzmann method.

Considerations on the Use of StarkBroadening. Stark broadening has beenplaying a central role in LIBS predom-inantly because it is largely used for theevaluation of the electron number den-

sity. A very large number of papers dealwith this topic.43,92,136–198 It is worthnoting that all the knowledge acquiredwith the evaluation of ne in non-laserplasmas has been directly applied toLIBS plasmas. We summarize heresome basic remarks regarding the useof Stark broadening:136

� The linear Stark effect applies tohydrogen and the quadratic Starkeffect applies to non-hydrogenic spe-cies. The theoretical treatment eitherignores ion dynamic effects, e.g., inthe Kepple–Griem theory (KG), ortakes them into account, e.g., in theModel Microfield Method (MMM)and the l–ion model.136–140 Startingfrom the l–ion model, Gigosos andCardenoso (GC)141,142 have devel-

FIG. 3. Departure from local thermodynamic equilibrium (LTE) and from the‘‘single temperature’’ assumption. When the ground level is inserted in the ASDFplot, different slopes may be seen, corresponding to an ionizing or recombiningplasma. Reproduced from Ref. 104 (top left figure) and Ref. 107 (lower twofigures), courtesy of Elsevier, BV.


focal point

oped a computational model thatincludes the effect of ion dynamics.It is in fact well known that theinfluence of ions (which is usuallyneglected) produces extra broadening,in addition to asymmetry in the profileand line shift: such effects wererecently investigated for the Fe538.34 nm line in a plasma producedby a Nd:YAG laser on a 50% Fe-Nialloy (Bengoechea et al.186).� All hydrogen lines (Ha = 656.285 nm,

Hb = 486.133 nm, Hc = 434.047 nm,and Hd = 410.174 nm) have beenused. The Ha line is the most intense,but it is also the one that is mostaffected by neglecting the ion dynam-ics. In addition, the transition has anabsorption oscillator strength that is afactor of ~4 higher than that of Hb,

which may explain the self-absorptionproblems with the use of the former.� Hb is less intense but also only

modestly affected by ion dynamics,thus giving more accurate results. Athigh ne values (e.g., 1017–1019 cm-3),the use of Hb has problems due tospectral overlap from Hd and Hc sincethe line becomes too broad andasymmetric.� When the electron number density is

high, and remains above ~1016, notmuch influence is expected using theKG theory. If ne becomes lower thanthis limit, the use of Ha leads to anoverestimate of ne. This has the effectof smoothing the steepness of thedecay of ne versus delay time, whichhas consequences on the assumptionof LTE.

� The Stark shift can also be used, butStark shifts are usually smaller thanStark widths.

The literature reports the use of all Hlines. For example, Samek et al.172

indicate the Hb line as the first choiceand Hc as the second choice. Ha issuitable at low electron number densitybecause of the problem of self-absorp-tion. On the other hand, Calzada96

reports that at low ne values, Ha

overestimates ne when ion dynamicsare not taken into account. Moreover,Hb is too broad at high ne.

161 Wiese35

reports that Hb is highly attractive,having a FWHM of about 1 nm at ne

= 1016 cm-3 and about 0.2 nm at ne =1015 cm-3.

In addition to the hydrogen lines,which can originate from the sample orthe surrounding atmospheric water va-por, LIBS has the inherent advantage ofproviding many lines of the targetelements, which makes it easy anduseful to evaluate the broadening profileof some of these lines to retrieve ne.Because of the importance of usingmany lines for an accurate determinationof ne and of the difficulty in using someof the H lines (because of their lowintensity) without adding some hydro-gen to the plasma, several alternativetransitions are listed in Table VI.

In many cases, only one line is used.While this is sufficient for a quickestimate of ne to be compared with thevalue calculated by the McWhirtercriterion,19 when more accurate data arewarranted, e.g., to retrieve the spatial andtemporal distribution of ne, it is advis-able, and recommended, to use multiplelines and to compare the resulting ne

values with each other and with thatobtained with one hydrogen line.

A rapid, approximate, passive methodfor the simultaneous determination ofboth ne and Te was proposed112,167 andexploited for microwave plasmas. Themethod is based upon the measurement ofthe Stark broadening of two or more linesunder the conditions of the experiment. Itwas found that the functional dependenceof the electron number density (propor-tional to the Stark width) versus temper-ature is different for different lines: forexample, the Stark broadening increaseswith the electron temperature for the Hc

line while it decreases for the Hb line. As

FIG. 4. Plasma images and spectral profiles of two Ba II transitions. Self-reversalis clearly observed in the transition terminating in the ground state. The effectcan be seen for all integration times shown. It can also be used to calculate theplasma temperature (Ref. 169). (Heh-Young Moon, University of Florida,unpublished work.)


a result, it is possible to find the crossingpoint where the theoretical Stark broad-ening for Hc and Hb coincides with themeasured Stark broadening.112 The cross-ing point then determines the bestdiagnostic value for ne and Te simulta-neously.

Considerations on the InstrumentalFunction. Pertinent to the Stark broad-ening data is the evaluation of theinstrumental function of the spectralapparatus. This is a well-known problemin emission spectroscopy, exhaustivelytreated in books (see, for example,Boumans,14 Alkemade et al.,15 andMontaser and Golightly16), reviews ofline profiles (see, for example, Refs. 199and 200), and specific articles on slitfunction effects (see, for example, deGalan and Winefordner201). Usually, theinstrumental broadening is experimen-tally found by scanning the emissionprofile of a line emitted by a low-pressure discharge (hollow cathodelamp) or a laser (usually He-Ne). Thesame holds in the case of LIBS.

When the dominant broadeningmechanism is considered to be Starkbroadening, Doppler broadening, andvan der Waals and resonance (Holts-mark) broadenings, the overall profileshould be given by the convolution of aGaussian part, due to the Doppler profileand to the instrumental function, andthree Lorentzian profiles, i.e., the Starkprofile, the van der Waals profile, andthe Holtsmark profile. The addition ofthe three Lorentzian profiles is thenlinear while the two Doppler profilesadd quadratically. The overall profile isusually described by the Voigt func-tion.43,96,112,171 In the LIBS literature,Stark broadening is considered domi-nant and two different approaches canbe found for the instrumental function.In the first approach (see, for example,Refs. 112, 176, and 185), the instru-mental broadening is described by aGaussian profile, and the true profile ofthe line is then obtained by the quadraticaddition of the two, i.e.,

Dkmeasured=DkStark

2

� �

þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

DkStark

2

� �2

þðDkinstÞ2" #vu

ut ð4Þ

In the second approach (see, for exam-ple, Ref. 198) both Stark and instrumen-tal profiles are considered as Lorentzianfunctions and are therefore added line-arly. In this case, the true profile isobtained by a simple linear subtractionof the instrumental profile, i.e.,

Dkmeasured=DkStark þ Dkinst ð5Þ

Both of the above assumptions havebeen used. We note, however, that in thecase of Lorentzian and Gaussian pro-files, linear subtraction is not cor-rect.203,204 Clearly, the experimentalprofile is represented by a convolutionof the two functions, and suitable de-convolution procedures should thereforebe used to retrieve the true profile. Forgrating monochromators, one should

also be aware of the fact that spectralbandwidth varies with wavelength.Moreover, the instrumental function isneither completely Gaussian nor Lor-entzian202 (see Fig. 6) and thereforeneeds to be measured for every setup.

Finally, one should note that rele-vance of the correction of the measuredprofile for the instrumental function willbe different at different delay times,being negligible at early delays, whenthe Stark effect dominates, and moresignificant later in time during theplasma evolution, due to the decay ofthe electron number density. In the lastcase, the other causes of broadening(i.e., Doppler, van der Waals, andHoltsmark resonance), need to be con-sidered and corrected for.

At long delay times, where all the

FIG. 5. Illustration of the line-to-continuum approach. In this experiment, thecontinuum can be measured accurately only up to 2–3 ls delay from plasmaformation. The difference between the electron temperature and the excitationtemperature decreases as the delay time increases and vanishes around 5 ls.(Heh-Young Moon, PhD Thesis, University of Florida, Gainesville, Florida, 2010.)


focal point

broadening contributions are much lessthan the instrumental broadening, the slitfunction can be obtained directly fromthe line emission profile.187

We finally note that, as pointed out byKonjevic,43 in the case of asymmetricbroadening, which is the case for neutralatom lines, the deconvolution procedureneeds to be different from that used inthe analysis of Voigt profiles.

Calibration of the Detection System.Except in rare cases, in which twotransitions are within a spectral rangecharacterized by a constant optical-detector response,147 the detection sys-tem, involving both the collection op-tics, the monochromator, and the photondetector, needs to be calibrated, since itsoverall response will vary with wave-length. This is accomplished with theuse of a standard lamp.

Some considerations are worth beingstressed here. First, most papers dismiss

the calibration process with one simplesentence stating that the system has beencalibrated with a standard lamp. Notmuch information is provided as towhether the lamp is a standard ofspectral irradiance or radiance, whetherit has a filament or a ribbon, and what itsoperating current, polarization, and tol-erances are. The impression given is thatcalibration is necessary, but trivial.Second, in addition to providing nodetails about the lamp itself, no exper-imental details on how the calibrationwas performed are usually given either.For example, how was the contributionof stray light in the UV and ofoverlapping orders in the visible mea-sured and corrected for, or which werethe characteristics of the power supplyand of the current/voltage measure-ments, and what are the estimates ofthe overall accuracy of the calibration.

Some exceptions exist. Yubero et

al.205 have addressed the calibrationissue and described the use of a halogenlamp, which is less expensive than thecalibrated NIST tungsten ribbon lamp.Absolute calibration requires a standardof spectral radiance (as reported byWiese35). Tashuck et al.,206 in theirradiometric calibration, used a pulseddiffusely scattered source and a tungstenlamp.

It is somewhat surprising that, con-trary to the field of non-laser-basedplasma spectroscopy, no systematicattempt has been made to use the classic‘‘branching ratio’’ method,207–212 whichmakes use of many well-characterizedspectral transitions emitted by the plas-ma, thus avoiding the use of externalcalibrated sources. The approach con-sists of comparing the intensities ofoptically thin transitions originatingfrom the same level: the theoreticalbranching ratio (i.e., the ratio of theknown transition probabilities) is mod-ified by the differences in the spectralresponse of the detector. This is espe-cially relevant in the low UV andvacuum-UV, where the radiant outputof the standard lamps is insufficient orlacking. Branching ratios for the Ar IItransitions in a wide wavelength range(~210–4590 nm) have been pub-lished.207–209 In ICP work, Doidge210

reported branching ratios for the ele-ments Fe, Se, Te, Ge, and Pd.

A detailed description of the relativeand absolute calibration procedure of abroad band echelle spectrometer hasbeen recently described by Bibinov etal.211,212 In LIBS work, using an echellespectrometer, Rehse and Ryder213 havemeasured the branching ratio fromhundreds of transitions of singly ionizedNd and Ga, although the focus of thework was not the calibration of thesystem.

To our knowledge, the only paperusing the branching ratio of Ar spectrallines in a plasma formed on a gold targetis that of Ortiz and Mayo.181 Therefore,in concluding these remarks, it is feltthat the issue of calibration deservesmore careful attention.

A Self-Consistency Check of LTEUsing Several Connected Methods. Adiagnostic self-consistency approach forchecking the existence of LTE condi-tions in the plasma can now be suggest-

FIG. 6. Stark broadened profiles, used to evaluate the electron number density.The spectral width of the profile decreases by increasing the delay time, andother broadening effects, including the slit function, need to be taken intoaccount. The figure on the left is reproduced from Ref. 202, with permission).


ed (see Fig. 7). It consists of a sequenceof steps that are linked to each other: alltogether, they constitute a valid multi-methodological test to assess how closethe plasma status is to LTE.

Note that the above sequence appliesto one given delay time and to one gateintegration time. Ideally, the temporalevolution of the physical parametersmeasured in the various steps shouldbe followed by varying both of theabove time parameters. Also, note thatall the methods proposed are passiveand, with the exception of (2), indirect.

The proposed steps are as follows:

(1) Because Stark broadening does notdepend upon the existence of LTEconditions in the plasma (although,strictly speaking, the broadeningparameter depends upon tempera-ture, albeit weakly), measuring ne

should be the starting step.(2) Stark broadening of selected lines is

measured according to the targetinvestigated (see Table VI). Multiplelines should be used. If hydrogenlines are used, one should avoidadding H to the plasma, if at allpossible. If the delay time is tooshort, ne may be too high for the use

of Hb, which could be too broad forthe spectral range simultaneously

seen by the detector. We thencalculate ne using Eq. T4.22 or Eq.T4.24.

(3) The ratio of the intensities of anionic line to a neutral line (ion-to-

atom ratio, Eq. T4.16) is measuredfor an element present in the target ata concentration level to assureoptically thin conditions (no self-absorption). Spectral calibration ofthe detection system should be used,

if necessary. Additionally, the plas-ma temperature is measured with the

FIG. 7. Pictorial representation of several independent approaches used to check the existence of LTE in the plasma, inaddition to the mere use of the McWhirter criterion. The measurement of the Stark profile is supplemented by the line-to-continuum ratio and by the ion-to-neutral ratio. As expected, LTE seems to be better established at longer delays. (Heh-Young Moon, University of Florida, unpublished work.)


focal point

Saha–Boltzmann plot method (Eq.T4.31).

(4) ne is calculated from the ratiomeasured in (3) and its consistencywith the value given by the Starkbroadening measurement under (2)is checked. Alternatively, the Starkvalue of ne measured under (2) isinserted into the line ratio expres-sion and the deviation of the tem-perature value obtained in this waywith the Saha–Boltzmann tempera-ture measured under (3) is calculat-ed.

(5) From the values of the intensity ratioand the Saha–Boltzmann tempera-ture measured under (3), a graph isconstructed by plotting the log of theion fraction versus the ionizationpotential of several elements presentin the target. From the intercept ofthis plot, ne is calculated and thisvalue is compared with the Starkvalue obtained under (2). The sameexercise can be done for T, i.e., fromthe intensity ratio and ne, T iscalculated from the intercept of thegraph and compared with the Saha–Boltzmann value.

Considerations on the Use of Laser-Induced Absorption and Fluorescencein LIBS. The following discussion is acompendium of the main features out-lined in several of the papers mentionedin Table VII, which also adds somecomplementary information and obser-vations on each of the approaches.

Absorption measurements in LIBSplasmas can be envisaged in differentways. One way is to use a fixedfrequency laser (for example, the samelaser that created the plasma) anddirectly measure the plasma transmis-sion:226,227 this allows one to draw someconclusions about the mechanism ofenergy absorption at the early stage ofplasma formation (e.g., multi-photonionization and inverse bremsstrahlung).Another way is to use an external,tunable laser traversing the plasma atdifferent delays with respect to plasmaformation.228–230 The laser can be ex-panded and encompass the entire plasmavolume or it can be collimated with adiameter much narrower than the plasmaheight, thus allowing spatially resolvedmeasurements in the vertical plasmadirection (time-of-flight measurements).

When the spectral profile of the laser ismuch narrower than the absorptionprofile of the atomic (ionic) transitioninvestigated, the spectral shape of thetransition can be directly obtained byscanning the laser wavelength across theentire profile228 and the number densityof the absorbing species can be evalu-ated. A final way is to use the plasmaitself as a continuum radiation source forthe absorbing species.231 This can bedone using the LIBS plasma as anexternal excitation source and focusingits radiation on the atom reservoir; inthis way, the laser-induced plasma playsthe role of the primary excitation sourcein a conventional atomic absorptionexperiment.231 It is interesting to notethat by analyzing the plasma emission atearly times (less than ~ 100 ns), whenthe spectral continuum dominates thespectrum, one notices atomic absorptionfeatures corresponding to strong transi-tions involving the ground state or low-lying levels (this would be a sort ofFraunhofer absorption spectroscopy).

The last approach has been recentlyexploited by Ribiere and Cheron232 byusing two lasers to produce two closelyspaced, independent plasmas on thesame sample and investigating theresulting absorption features at differentinter-pulse delays. The authors reportedspatially resolved absolute number den-sities of species and were able to followtheir temporal evolution during theplasma expansion.232

The most important advantage oflaser absorption methods is that theydo not require LTE assumption toprovide absolute number densities: thisis different from an absolute emissionmeasurement, which relies upon LTE.The knowledge of the absorption oscil-lator strength, however, is still required.In addition, no calibration of the detec-tion system is needed, the only require-ment being that the interaction betweenthe laser radiation and the atoms must belinear.

In conclusion, an absorption experi-ment is capable of providing absolutenumber densities, spectral line widths,and plasma expansion velocity. Inaddition, imaging techniques can beimplemented to provide vertically re-solved vertical distributions of longitu-dinally averaged atomic and ionic

populations. It is therefore somewhatsurprising that absorption experimentswith tunable laser sources have not beenso popular in LIBS work.

Fluorescence obviously relies on ab-sorption as a primary excitation step.The advantage of fluorescence measure-ments in general is that, unlike emissionand absorption, which provide line-of-sight averaged data, they provide localinformation, the spatial resolution beinglimited by the minimum laser excitationvolume in the plasma resulting in asufficient signal-to-noise ratio. The tech-nique is capable of evaluating numberdensity and temperature.233 In bothcases, the fluorescence signal can beobserved from the same atomic (ionic)level reached by the laser excitation(resonance and direct line fluorescence)and from nearby levels populated bycollisions. From an absolute measure-ment for a given transition, the numberdensity of the emitting atoms (ions) iscalculated, in much the same way as it isdone for emission measurements. Whenrelative, rather than absolute, measure-ments are performed, relative numberdensity profiles are obtained.234–239

As in the absorption case above, if aspectrally narrow tunable laser is avail-able, and the optical interaction betweenthe laser and the atoms (ions) is linear, afluorescence excitation profile, obtainedby keeping the fluorescence monochro-mator fixed at the center of the transitionwhile slowly scanning the laser wave-length across the line, directly gives thespectral profile S(k) of the transition.Care must be taken here to avoid anyspurious broadening effect, which wouldoccur if the laser–atom interaction isnonlinear (saturation broadening). Thisprocedure has the additional benefit that,when the monochromator is set at thelaser wavelength and the scanningprocedure is repeated, the resultingprofile directly gives the instrumentalslit function.

It is well known that, with strong laserexcitation, the transition can be opticallysaturated: this results in an improvedsignal-to-noise ratio and the additionaladvantage that the signal is independentof the collisional quenching between thetwo levels coupled by the laser. Both ofthese statements have to be taken withcare: under saturated conditions, the


TABLE VII. Laser-induced atomic absorption and atomic fluorescence approaches to plasma diagnostics.a

Approach Outcome Comments Selected referencesb

Fixed frequency laser transmissionmeasurements in the plasma

Energy absorption mechanism:photo-ionization versus inversebremsstrahlung

Useful at early delay times (,100 ns),when ne is large enough to make thelaser and plasma frequencies closeenough for absorption, rather thanscattering, to be the dominateinteraction process.

Song226; Hohreiter227

Resonance absorption with tunablelasers

Line profiles; absolute numberdensity; plasma expansionspeed; plasma temperature

Laser must be spectrally narrower thanthe absorption profile. Integratedabsorption is directly proportional tonumber density. Plasma imagingprovides spatial information.Temperature can be indirectlyevaluated from number density.

Gornushkin228,229; Lokajczyk230

LIBS continuum atomic absorption Transient atomic and molecularabsorption spectra; absolutenumber density

Conventional atomic absorptionspectroscopy where the primarysource is the LIBS continuum. Ifcoupled with a high spectralresolution monochromator, numberdensities can be obtained.

Xu231

Double-LIBS atomic absorption Absolute number density Two lasers and two plasmas close toeach other on the same sample. One-dimensional radiative transferequation provides spectral profilesand number density.

Ribiere232

Single-step excited, spectrallyintegrated, time-integrated resonanceand direct line fluorescence

Spatially resolved number densityprofiles; plasma imaging;diffusion data

Single laser excitation. Scatteringproblems for resonance fluorescence.Optical saturation welcome toimprove signal levels (in absence ofscattering). Absolute number densityproblematic.

Niemax234; Sdorra235; Dutouquet236;Meng237; Tsuchida238; Martin239;Matsuo240

Single-step excited, spectrallyintegrated, time-resolved, resonance,and direct line fluorescence

Lifetime of excited states reachedby laser excitation

Single laser excitation. Scatteringproblems for resonance fluorescence.Optical saturation not necessary butwelcome. For LIBS work, short laserpulses (,~5 ns) are needed.

Measures241; Van der Heijden242;Uchida243

Single-step excited, spectrallyintegrated, time-resolved, collision-induced fluorescence

Collisional relaxation rates;electron number density;excitation temperature

Direct evaluation of the collisional ratesof (de-)population of excited levels.Rate equations approach needed tocharacterize the system. r and ne canboth be evaluated. In LIBS, levelscan be observed at large DE values(2–3 eV) above or below the laser-pumped level.

Burrell244; Denkelmann245;Tsuchida246; Dubreuil247; Breger248;Dzierzega249; Zizak250

Emission-fluorescence ratio and two-line fluorescence ratio

Excitation temperature Single-step excitation. Saturationneeded. Time resolution not essentialbut welcome. Method assumes LTE.

Kunze251; Bradshaw252

Two-photon excited fluorescence (two-photon absorption-LIF); double-stepexcitation

Spatially resolved number densityprofiles; excited-state lifetimes

Populating highly excited states ispossible. Two-photon excitationrequires a single laser, while twotunable lasers are used in double-stepexcitation.

Dobele233; Van der Heijden242;Omenetto255

Pump and probe fluorescence Ionization fraction; temporalevolution of ions

Two or more lasers needed (two needto be tunable). Variable time delaybetween lasers is also needed. InLIBS, issues arise due to the plasmanot being stationary.

Turk253; Omenetto41

Simultaneous multi-method approaches(absorption-emission-fluorescence)measurements

Three-dimensional numberdensity of species; spatiallyresolved temperature

Simultaneous absorption andfluorescence, e.g., Ba II,256 Mg (I)and (II);257 imaging, absorption,emission, and ion probe (Y, Ba);258

emission and single-frequencyabsorption.259

Al-Wazzan256; Martin257; Geohegan258;Kearny259

a This table reports several approaches that have been used, or could be used, in order to evaluate physical parameters of various plasmas, not limited to laser-inducedplasmas. Emphasis is given here to the diagnostic rather than the analytical aspect of the atomic fluorescence technique: the last aspect will be addressed to in oursecond paper.57 For a general introduction to laser-induced atomic fluorescence spectroscopy, the reader may wish to consult the following monograph: N. Omenettoand J. D. Winefordner, ‘‘Atomic Fluorescence Spectrometry–Basic Principles and Applications’’, Prog. Anal. At. Spectrosc., vol. 2 (1,2) Pergamon Press (1979).

b This column reports the name of the first author appearing in the reference cited.


focal point

signal-to-noise ratio can in fact degradeif spurious scattering of the laser lightenters the detection system, and thequenching independence holds at thepeak of the fluorescence waveform, thusimposing the necessity of performingtime-resolved measurements, with thecorresponding need of a more sophisti-cated acquisition routine. This increasedcomplexity, on the other hand, has theadded benefit of providing informationabout the plasma excitation-ionizationdynamics.

Various papers describing fluores-cence diagnostics in plasma are avail-able (for example, see Refs. 234 through249, and the information provided inTable VII ) . Exci ted-s ta te l i fe-times,241–243 obtained by measuring thefluorescence decay after the laser pulseis terminated, is indeed a useful param-eter when measured at different delaysafter the formation of the plasma: asdiscussed by Measures et al. back in1977,241 its temporal behavior providesdirect information about electronquenching and self-absorption effects.The time lag observed in reaching thepeak of the signal when collisionallyinduced fluorescence is compared withdirect line fluorescence provides infor-mation about the excitation rates andassociated cross-sections;244,245 viceversa, if the cross-section is known orcan be calculated, the ratio between thefluorescence signals resulting from di-rect coupling and collisional couplingcan be used to evaluate the electronnumber density.246–249

Tunable laser excitation can enhancethe population of several excited levelswithin its accessible wavelength range.The resulting collisional coupling allowsthe observation of fluorescence signalsoriginating from all levels lying even afew eV below and above the leveldirectly reached by the laser. A Boltz-mann analysis, made at different delaytimes from the onset of the plasma, canthen be used to evaluate the excitationtemperature, similar to what was done inflames by Zizak et al.250

Finally, a time-integrated, saturatedfluorescence signal observed at a given(adjustable) time within the emissionwaveform (see Fig. 8) can be comparedwith the emission signal and the ratioused to calculate Texc.

251 In this case, a

Boltzmann equilibrium between theinitial and final state of the transition isassumed. The temperature derived fromthe saturated fluorescence signal canthen be compared with the value ob-tained with the Boltzmann plot. Notethat there is no need for the transitionprobability or for the calibration of thedetection system.

Several other papers discuss thecombined use of LIF and LIBS. How-ever, the main target was improving theLIBS sensitivity rather than performingdiagnostic measurements of the plasmaparameters. These papers will be report-ed and discussed in our second focusarticle.57

In LIBS, the use of fluorescence, andin particular of time-resolved fluores-cence and pump–probe fluores-cence,253,254 has not become popular.Understandably, this is due to thecomplexity of the plasma composition,which makes difficult the assignment ofa cross-section to one specific process,to the need of continuously tunablelasers, and to the low signal-to-noiseratio achieved when working with fastdetectors and associated electronics inorder to provide nanosecond time reso-lution.

Absorption, emission, and fluores-cence can be used simultaneously with-out adding instrumental complexity tothe system. Indeed, this multi-methodo-logical approach has been successfullyused to map number density of speciesand to characterize plume dynam-ics256–259 (see Table VII).

In concluding this subsection, wewould like to point out that the word‘‘fluorescence’’ should not be used todescribe LIBS experiments alone. Thereare cases (e.g., photo-fragmentation,resonant laser ablation) in which onecould justify the use of ‘‘laser-inducedplasma fluorescence’’ instead of ‘‘laser-induced plasma emission’’. This seman-tic issue will be addressed in the secondarticle.57

THE ISSUES OF LOCALPLASMA PERTURBATION:PLASMA–PARTICLEINTERACTION

The LIBS methodology makes use ofthe laser-induced plasma to vaporize anddissociate a targeted material, which

may originate from the gaseous or liquidstate, but more commonly originatesfrom the solid state. We focus here onthe former two, which therefore neces-sitates the transformation of the targetedanalyte species from discrete volumes ofmass (e.g., droplets, bulk solid, orparticulates) to individual, dissociatedatoms and ions undergoing atomicemission. In preceding sections, theimportant processes of laser samplingand atomic excitation and emission havebeen reviewed. What is left to discusshere is the associated physics of heat andmass transfer as related to the original,discrete volume of sampled mass cou-pled with the finite quantity of energywithin the laser-induced plasma andmore importantly, the relatively com-pressed temporal scales associated withLIBS. Given the presence of an initialquantity of mass (e.g., an ablationparticle), which will nearly alwayscontain large numbers of atoms inaddition to the analyte species ofinterest, one must consider the role ofconcomitant mass on the physics ofcomplete particle vaporization and ulti-mately on the analyte response withinthe plasma.

In the analytical community, suchbehavior would fall under the label ofmatrix effects, a topic of considerabledepth and complexity that remains at thecore of quantitative analysis for manyanalytical schemes, including LIBS. Thetopic of matrix effects will be treated inthe second article;57 however, it is usefulto shed light on this topic via interac-tions of introduced analyte mass withthe laser-induced plasma at relevantspatial and temporal scales.

For this discussion, we will use theterm particle to refer to discrete massesof targeted material that interact with theplasma, recognizing that these ‘‘parti-cles’’ may arise from laser ablation,microdroplets, aerosol samples, etc.The phrase plasma–particle interactionsimplies an interaction between theanalyte-containing particle and the la-ser-induced plasma, rather than betweenthe particle and the laser beam. This isan important distinction that arises fromconsideration of the relative spatialvolumes characteristic of the laser focalvolume and the resulting laser-inducedplasma. The latter is typically several


orders of magnitude greater than the

former, which directly translates to a

greater probability of plasma–particle

interactions as compared to direct la-

ser–particle sampling. Of course, for

high particle loadings, the laser will

inevitably directly impact particles, but

the vast majority of events will be

interactions with the highly dynamic,

laser-induced plasma. This is verified in

the context of plasma volume measure-

ments, particle sampling rate consider-

ations, and direct imaging studies.260–263

The plasma–particle processes must also

be framed in the context of the overall

plasma lifetime (~10–100 ls for typical

pulse energies) and the analytical time-

scales (i.e., detector delays and gates),

which typically range from ~1–50 ls

following the initial laser pulse.264

With this framework in mind, Fig. 9

describes the physical processes that

govern the dissociation of constituent

species within the laser-induced plasma

in the context of analyte signal linearitywith increased analyte concentration,

and on the independence of the analyteatomic emission signal from concentra-tions of other species. From a physicspoint of view, these concepts may beextrapolated to the context of rates ortimescales of heat and mass transfer.54 Ifthe timescale for complete analytevaporization and dissociation is muchless (i.e., an order of magnitude faster)than the analytical measurement time-scale, these processes may be consideredessentially instantaneous, and the atomicconcentration might be expected to scalelinearly with analyte mass. If thetimescale for diffusion of heat from theplasma to the localized region of analytemass and the timescale for diffusion ofanalyte mass into the plasma are alsomuch less than the analytical measure-ment timescale, then the analyte spatialdistribution, excitation, and ensuingatomic emission should correspond tothe overall plasma conditions (i.e., bulkor spatially averaged), such that nolocalized perturbations to the plasmastate in the vicinity of the analyte massoccur due to the presence of a vaporiz-ing analyte particle.

The above scenario corresponds to theideal situation, in which particle-derivedanalyte species interact uniformly withan unperturbed, analytical laser-inducedplasma. In reality, such a scenario is notachieved, but rather, research has shownthat the timescales of particle vaporiza-tion and dissociation, and the timescalesfor heat and mass transfer, are allcomparable to the typical analyticaltimescales of plasma evolution. Toquantify such phenomena, researchersturned to spatially resolved spectralmeasurements and direct plasma imag-ing. Hohreiter and Hahn260 were the firstto directly image analyte species in alaser-induced plasma, as calcium atomsvaporized and dissociated from anindividual glass microsphere and subse-quently diffused into the surroundingplasma. Their study provided directevidence of the actual timescales ofparticle vaporization and analyte diffu-sion, revealing that the plasma–particleinteraction is initially limited to alocalized spatial region about the ana-lyte-containing particle. Analysis yield-ed diffusion coefficients of the calciumatoms on the order of 0.05 m2/s over theplasma timescales of 2 to 30 ls

FIG. 8. Plasma emission (Ba II, Ca II, and Sr II) and laser-induced fluorescence(Pb I) images obtained by forming the plasma on a glass target (top image). Thedye laser (283.305 nm) is focused with a cylindrical lens. The trace below, takenwith a PMT, shows the temporal evolution of the Pb atomic emission (405.781 nm)and transient enhancement resulting from dye laser excitation. (Dan Shelby,University of Florida, unpublished work.)


focal point

following plasma initiation and a time-scale of ~15–20 ls for completedissociation of the 2-lm glass micro-spheres. In related studies, Buckley etal.265–267 explored the influence of thespatial location on the atomic emissionfrom aerosol particles in laser-inducedplasmas. Their spatially resolved spec-tral measurements revealed a variabilityin analyte signal with the location ofparticles within the plasma.

The above studies document thepresence of spatially localized analytespecies with laser-induced plasmas andtherefore raise the question of theimportance of localized plasma pertur-bations due to loss of plasma energy tovaporization and dissociation processes.Previous studies revealed no changes to

the bulk plasma properties (i.e., spatially

averaged plasma), namely excitation

temperature and electron density, due

to the presence of discrete particles.268

Diwakar et al.124 examined the issue of

localized plasma perturbations by exam-

ining the analyte signal from a range of

multi-component submicrometer-sized

aerosol particles. Analyte species exam-

ined included sodium, magnesium, and

cobalt with the addition of the elements

copper, zinc, or tungsten at mass ratios

from 1:9 to 1:19 (analyte-to-concomitant

species). They found a perturbation in

localized plasma state, as measured by

changing atomic emission intensity and

ion-to-neutral ratios, which was attribut-

ed to the loss of plasma energy required

to vaporize and ionize the aerosolparticle mass.

The above studies provide directevidence of a matrix effect, as theresulting analyte signals were affectedby additional particle mass. An impor-tant finding in the Diwakar et al.study,124 however, was that the resultingperturbations to analyte response wereminimized at longer plasma delay times(~60 ls), which is attributed to theallowance of sufficient time for theanalyte atoms to thoroughly diffusethroughout the plasma and for heat todiffuse into the regions of the originalparticle dissociation, thereby equilibrat-ing the analyte atoms with the overallbulk plasma conditions. Taking thesestudies in aggregate, it is concluded that

FIG. 9. Physical processes governing the dissociation of constituent species within the laser-induced plasma. Localperturbations of plasma parameters occur while heat is transferred to the particle and mass is transferred to the plasma. Inthis context, the timescales for the diffusion of heat and mass govern the overall plasma conditions and provide directevidence of the matrix effect.


quantitative LIBS analysis should beperformed with careful attention givento the temporal plasma evolution andanalytical timescales, noting that thefinite timescales of particle dissociationand heat and mass transfer are allequally important.

Experimental studies have providedmuch insight into the plasma–particleinteraction issues, but complementarynumerical simulations and modelingstudies can provide additional valuableinsight into overall laser-induced plasmadynamics.47,125,269–274 A study by Da-lyander et al.125 specifically addressedthe timescales of heat and mass transferwith laser-induced plasmas for discretemass loading. The model includedsimultaneous solution of the heat andmass transfer equations using physicalmodels for the plasma thermal conduc-tivity and for the mass diffusivity of theanalyte species calcium and magnesium.The analysis revealed significant speciesgradients, attributed to the finite-scalesof mass transfer, and localized temper-ature perturbations attributed to energyrequirements of particle dissociation andionization. A very useful non-dimen-sional parameter for directly comparingthe timescales of heat and mass transferis the Lewis number, defined as the ratioof the thermal diffusivity to the massdiffusivity. Based on the diffusion ofboth the calcium and magnesium atomsin the Dalyander et al. study,125 theLewis number ranged from about 1 to 4,with an average value essentially unityfor plasma delay times beyond 5 lsfollowing breakdown.

Overall, these findings are in excellentagreement with the experimental resultsdiscussed above and indicate that thetime scales of heat and mass diffusionare comparable and finite. Accordingly,such a near-unity Lewis number isindicative of a finite rate of diffusionof heat into the region of particledissociation and of a comparable, finite,rate of diffusion of analyte species awayfrom the particle region. Such a scenariois consistent with the concept of initialsuppression of local plasma temperature,as energy that is utilized for particledissociation can only be replaced over afinite timescale by the inward diffusion(i.e., conduction) of heat.

In concert, the above discussion

suggests a link between single-particleLIBS and single-particle ICP-OES orICP-MS. In fact, the role of the laser isto create a plasma, in which the ensuingplasma–particle interaction effectivelycreates single-particle sampling andanalysis events,275–277 in much the sameway as single droplets are introducedinto the central channel of an ICP andthe temporal fate of the droplet followedby the resulting atomic emission [see,for example, the recent work of Groh etal.,278 in addition to the seminal workperformed by Olesik (see, for example,Ref. 279) and Hieftje (see, for example,Ref. 280)]. The sequence of eventsinvestigated (desolvation, vaporization,dissociation, excitation, ionization, anddiffusion out of the observed volume) isthe same in both cases, while the timeevolution and the dynamic effects fromthe different analytical plasmas aredifferent. The extrapolation of the aboveconcepts to laser ablation–ICP studies(LA-ICP-OES and LA-ICP-MS) isstraightforward. In such ‘‘tandem’’ ap-proaches, the laser has the role ofcreating the particles that are transportedin the ICP; hence, the processes ofparticle formation and plasma formationare independent.

Ultimately, the most important out-come of the study of plasma–particleinteraction is that any advances in ourunderstanding of the fate of an analyte-containing particle entering the plasmawill have a direct beneficial repercus-sion on the analytical use of LIBS, LA-ICP-OES, and LA-ICP-MS. Clearly thephysical processes as outlined abovegovern the subsequent analyte response.Only through understanding and appre-ciation of these processes can LIBS andrelated plasma-based analytical schemesbe optimized to realize their full analyt-ical potential.

CONCLUSIONS

In this article, a review of the varioustopics and techniques used for thespectroscopic characterization of plas-mas has been given. The discussion hasbeen focused on the use of manydiagnostic approaches, involving themeasurement of atomic and ionic emis-sion, absorption, and fluorescence, inaddition to scattering methods. Severaltheoretical expressions relating the emis-

sion signal to the plasma parametershave been given. These expressionsinclude the measurement of line inten-sity, line profiles, ion-to-neutral ratios,and line-to-continuum ratio. Moreover,their application to the evaluation ofelectron number density and plasmatemperature has been discussed. Addi-tional, complementary information hasbeen collected in tables, together withpertinent literature citations.

The important issue of plasma–parti-cle interactions and the resulting localperturbation of the plasma has beendiscussed, showing that the time scalefor the diffusion of heat (from theplasma to the particle) and mass (fromthe particle to the plasma) govern theoverall plasma conditions.

The focus of this article is on laser-induced plasmas: nevertheless, referenceto previous pertinent knowledge ac-quired over many decades of work withnon-laser plasmas, such as arcs, sparks,discharges, microwave-induced plas-mas, and inductively coupled plasmas,has been systematically made, with thehope that it will serve as a trigger forreaders to benefit from it and to applysome unexplored diagnostic approachesto LIBS. Indeed, the problems encoun-tered in diagnostic LIBS work are nodifferent from those reported with otherplasma sources and are aggravated bythe transient nature of the laser-inducedplasma. The similarity is perhaps bestdemonstrated by referring to the articleby Huang and Hieftje,134 in which theauthors state that the key question:‘‘What are the most useful fundamentalparameters for characterizing the behav-ior of the inductively coupled argonplasma?’’ has the following answer:‘‘Local electron temperature, electronnumber density, and gas-kinetic temper-ature’’.134

The second part of this review willfocus on the quantitative aspects ofLIBS, discussing problems related tocalibration, matrix interferences, detec-tion limits, advances in instrumentation,and data processing.

ACKNOWLEDGMENTS

This work was supported by the NationalScience Foundation through grant CHE-0822469,as part of the Plasma-Analyte Interaction WorkingGroup (PAIWG), a collaborative effort of theUniversity of Florida, the Department of Analyt-


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ical Chemistry and Reference Materials, FederalInstitute of Materials Research and Testing (BAM)in Berlin, and the Institute for Analytical Sciences(ISAS) in Dortmund, jointly funded by the NSFand DFG. We would like to thank our graduatestudents and Dr. Ben Smith for many usefuldiscussions.

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